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Foundations of Statistics
4th Edition
Dr Glenda Francis
Dr Andi Garing
Module 1 Critical Thinking in Statistics
MODULE1
Introduction to Critical Thinking in Statistics
In both your personal and your professional life you'll often come into contact with statistics.
Open a newspaper, surf the internet or turn on the radio or the television and you're going to
fmd examples - anything from an advertising campaign trying to convince you to use a
particular anti-dandruff shampoo, to a report on the strength of opposition to some
government policy. Did you know that Labor voters prefer to watch soapies, while Liberal
voters prefer cop shows? Can this be true? - well according to a report I heard on the radio, it
is - but should I believe them? Some statistics reported in the media defmitely come into the
category of'lies, damned lies and statistics'but some represent well conducted studies with
important consequences. How can we tell which is which? One of the aims of this text is to
convince you of the value of good statistical studies while proofmg you against being misled
with statistics.
Throughout this text you'll meet a lot of statistical'jargon'. The language in statistics is very
precise, and terms you thou迦 you understood, like'population'and'significant', are used in
rather different ways in statistics to how they are used in everyday English. So in some ways
learning about statistics is like learning another dialect and your language skills will be far
more important than your mathematical skills.
1. 1 Statistics in Everyday Life

Statistics is all about answering questions. Let's briefly look at a couple of statistical studies
which have had a positive effect in our society. We're all aware that alcohol affects skill, and
this finding has resulted in laws against drink driving which have led to a reduction in the
road toll. The studies which established the effects of alcohol on driving skill were analysed
with statistics, and it was these statistics which convinced the politicians to act. Another
outstanding example of statistics being put to good use is in the search for causes of sudden
infant death syndrome (SIDS). Using statistical techniques researchers were able to identify
several risk factors for SIDS. Raising public awareness of these risk factors has substantially
reduced the incidence of SIDS.
"Awareness of the risk factors, and programs encouraging people to avoid the risk factors -
especially those aimed at getting parents to sleep babies on their backs - has resulted in a
70 per cent drop in SIDS cases over the past decade in Australia."1
1 . 2 Detecting Bias
So what distinguishes the good statistical studies from the bad? Let's start by looking at a
research question of our own, and explore how we might go about answering it. In 2000, 60%
of Australians reported having access to a computer at home. Has this percentage increased?
How would we go about answering this question? We could start by asking some people if
they had access to a computer at home. Suppose we put this question to a group of people and
recorded their responses. Rather than trying to analyse the data by hand, we'll use a statistical
package SPSS2, an IBM company —IBM SPSS Statistics release 23 (2015)3, (SPSS stands for
' Statistics Package for the Social Sciences'.) You'11 find instructions for using SPSS in
Appendix A, here we'll just show you the output and how to interpret it.
Peter Lavelle published 29/05/2003, http://www.abc.net.au/health/library/stories/2003/05/29/1831797.htm

2 IBM SPSS Statistics was formerly called PASW statistics
IBM Corp. released 2015. IBM SPSS Statistics for Windows, Version 23.0. Armonk, NY: IBM Corp.
Copyright ©2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. Andi Garing, Foundations of Statistics, 4th Edition
computer at home?
computer at home? • yes

口 no
Valid yes
Percent
88.3
I Valid Percent
88.3
l Cumulative
Percent
88.3
no 11.7 100.0
Total 100.0
So in this sample of 103 people, 8~.3% had a computer at home. That's a lot more than the
60% of Australians who reported having a home computer in 2000. Is this enough
information to convince you that the ownership of home computers has increased? This
question raises some important issues.
Populations and Samples

We are not just interested in the 103 people in our sample, we are interested in all adult
Australians. In the language of statistics, our 'population' is'all adult Australians'. This is the
complete set of things we're interested in. This use of the word'population' may be a little
different to what you're used to. Typically, if you ask people to use the term'population'
they'll come up with a sentence like - "The population of Australia is 20 million". You're
probably also familiar with the word'population'in the context of "The population of
Australia is all of the people in Australia". In statistics, a population might be all of the people
in a country, or all of the people in the shire of Yarra Ranges, or all of the members of the
local golf club. It depends on the question we are trying to answer. Someone working for the
Yarra Ranges Shire Council might want to know if the residents of the shire are happy with
the weekly rubbish collection service. In that case, the population they are interested in is all
of the residents in the Shire. If the local golf club wants to know how early in the morning the
members would like the club rooms to be open, then the population they are interested in is all
members of the golf club.
In these examples the population is 'all of the people we are interested in', but populations are
not necessarily people. If we want to answer the question'what is the shelf life of evercell
batteries', then our population is all evercell batteries. If we want to investigate what
percentage of Singapore households own a private car, then the population of interest is all
Singaporean households. So the'units of analysis' for a population don't have to be people,
~hey can be batteries or households or anything else. At the start of any statistical
mvestigation it's important to identify what population you are interested in and what the
'unit of analysis'is.
~EXERCISE 1.1 (Solution on page 255)

For each of the following scenarios, what is the population researchers are interested in?
What is the unit of analysis?
a. An Indonesian tourism authority wants to know the average length of stay for overseas
tourists visiting Indonesia.
b. A marketing organisation wants to know what proportion of Singaporean households
have an air conditioner.
c. An enterprising 10 year old wants to know the average amount of pocket money the
children in his class receive.
d. A shampoo manufacturer wants to know how effective their product is at removing
dandruff.
e. A consumer group wants to know the average number of kilometres "Beauyear" tyres
last.
2
Copyright © 2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. Andi Garing, Foundations of Statistics, 4th Edition
Module 1Critical Thinking in Statistics
~EXERCISE 1.2 (Solutiononpage255)

In which of the following scenarios, do you think there is bias in the way the sample has
been selected? In each case, start by thinking about what population the researchers are
interested in.
a. The Australian Government wants to know what proportion of Australian wheat
fam记rs want to have a'single desk'for export wheat sales. They make a list of all
Australian wheat farmers and randomly select a sample of 100. Each of these 100
farmers are contacted by phone and asked for their opinion.
b. The Australian Government wants to know what proportion of Australian wheat
farmers want to have a'single desk'for export wheat sales. They put a questionnaire
on the Australian Wheat Board's website asking people's opinion and 45 people
respond to the questionnaire.
c. An Indonesian Tourism authority wants to know the average length of stay for
overseas tourists visiting Indonesia. They spend two hours one Saturday morning at
Bali International airport interviewing all people departing on international flights.
They interview 165 overseas tourists who are returning home at the end of their visit.
Other Sources of Bias

The way in which the measurements are made or the questions are asked can also introduce
bias into a study. If I was to ask students'how committed are you to your studies?'the
chances are I would hear that everyone was'very committed'- who's going to tell their
lecturer they're not particularly committed to their studies! If people are asked to report on
their own attitudes or behaviours they tend to give what they believe are socially acceptable
responses. There are some self-reported measures that are notoriously untrustworthy. Ask
people how much alcohol they drink, or how many cigarettes they smoke each week and the
responses just don't match up with sales of alcohol and cigarettes. People may be embarrassed
about their consumption of alcohol and so under-report it, or they may be genuinely unaware
of how much they're actually drinking. The same thing happens with cigarettes.
Another potential source of bias is the way the questions in surveys are phrased. In one study4
conducted in the United States, responses to two different questions were compared. When
people were asked 'Do you think the United States should allow public speeches against
democracy?' 75% agreed. But when the question posed was'Do you think the United States
should forbid public speeches against democracy'over half of the respondents (54%) thought
such speeches should be forbidden. So more than half the respondents thought they should be
forbidden but more than half also thought they should be allowed!
Several studies done on eye witness reports raise questions about how reliable eye witness
testimony is in court cases. One great experiment was to show people a video of a car crash. 5
Some of the participants were asked'About how fast were the cars going when they hit each
other?' Others were asked'About how fast were the cars going when they smashed into each
other?'The average speed estimate for the frrst question was 34.0 mph, the average speed
estimate for the second question was 40.5 mph. Quite a substantial difference!
4 For more information on subjective survey data, see Bertrand, M. & Mullainathan, S. "Do People Mean What
They Say? Implications for Subjective Survey Data" Economics and Social Behavior
5 Loftus, E. & Palmer, J. 1974 "Reconstruction of Automobile Destruction: An Example of the Interaction
Between Language and Memory" Journal of Verbal Learning and Verbal Behaviour 13, 585-589
4
Copyright © 2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. A ndi Garing, Foundations of Statistics, 4th Edition
Even the order in which questions are asked can have an effect. The response to'How happy
are you with life in general? ' might depend on what other questions the respondents have just
been asked. Previous questions might remind them of some aspect of their life they are
particularly happy (or u呻appy) with, which tends to colour their response to the'general
happiness'question.
Problems with the way measurements are taken or with the way questions are asked can
introduce substantial bias. These effects might be unintentional or deliberate, and they might
be obvious, as in a leading question'Should refugees be subjected to the appalling conditions
in detention centres?'or far more subtle.
Comment on any obvious bias in the following measurements.
a. A research organisation is conducting a study on healthy eating habits. In this study the
respondents are asked to report on the number of take away meals they ate last week.
b. In a study on healthy lifestyles, a nurse records the weight of each of the participants
each week.
c. A market researcher asks shoppers to try out a new product for cleaning glass surfaces.
After the trial he asks'Is this remarkable product better than your normal cleaner?'
d. A market researcher asks a sample of television viewers: "Do you enjoy life style
programs?"
When you're looking at a statistical report in anything from a newspaper to a scholarly

journal, you should start by asking where the report originated. Who sponsored the report?
Who conducted the study? A report indicating high levels of dissatisfaction with the
government's new industrial relations policy might be viewed with some scepticism if the
study was conducted by the Australian Council of Trade Unions. A report on the effectiveness
of a new medication for treating insomnia might have been far more convincing if the study
had not been funded by a pharmaceutical company.
That's not to say that reports funded by pharmaceutical companies or trade unions are
necessarily biased or misleading. With a properly conducted study the motivation of the
researcher should have no impact on the results, so a study conducted by someone with a
vested interest is not necessarily biased. But if the organisation conducting or funding the
study does have a vested interest in the results, you'll want information on exactly how the
study was conducted before accepting the reported conclusions. Even with the best of
intentions, the researcher might bring some unconscious bias into the study.
So what's the overall conclusion here? Whenever you are looking at the results from any
statistical study, you need to think critically. You should always be looking for possible bias.
Here are a few specific things to keep in mind:
1. How were the individuals or objects in the study selected?
2. Exactly what measurements were made or what questions asked?
Copyright©2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. A ndi Garing, Foundations of Statistics, 4th Edition

Abersville is a fictitious town situated in a beef producing region of Australia. The
Abersville Meat Industry Council (AMIC) are concerned that the consumption of red meat
in Australia has been declining over the past 5 years, leading to the closure of the local
abattoir. They commission a study to explore current attitudes towards red meat, in order
to convince the abattoir owners that the abattoir should be re-opened. The study was
conducted by some of the retrenched abattoir workers, who are in need of employment.
Interviewers go to the local Abersville shopping centre and interview some of the passing
shoppers. In order to bring people's attention to the fact that they 're doing a survey about
meat, they stand close to the butcher' s shop. They begin the interview by describing the
benefits ofred meat in the diet, then ask the following questions:
How often do you eat red meat?
1. Everyday
2. On 6 days of the week
3. On 4 days a week or less
The closure of the abattoir has destroyed the livelihoods of many people m our
community, do you agree that it should be re-opened?
1. Yes
2. No
When they analyse the data they report back to AMIC that 97% of the respondents eat
meat every day, and that 95% agreed that the abattoir should be re-opened. AMIC feels
very encouraged. In a letter to the owners of the abattoir they report that interest in red
meat is very high with 97% of Australians eating red meat at least once a day. They also
report that 95% of people support the re-opening of the abattoir.
List all the possible sources of bias you can see in this study. (I can see at least 8). As an
extension question, and a challenge for you —come up with an equally ludicrous scenario
involving even more bias than this one :-).
Samples versus Populations

When we collect data from a sample, we're usually more interested in what's happening in
the population, rather than what's happening in the sample. For example, when we calculated
the percentage of students in our sample who had access to a computer at home, it wasn't just
the 103 students in our sample that we were interested in. We really wanted to estimate what
proportion of all Swinburne students had access to a computer at home.
If the way we select our sample is biased, or if our measurements are biased, the sample won't
tell us anything about the population we're interested in. But what if we use a good unbiased
method of selecting our sample, and the measurements we make or questions we ask don't
introduce any bias; what can our sample tell us about the population? This is something we'll
spend a lot of time exploring, starting in Module 3. For now, let' s just say that the sample
gives us some idea about the population, but it can 't tell us precisely what' s happening in the
population. So if 88% of the students in our sample have access to a computer at home, then
it's reasonable to assume that the percentage of (all) Swinburne students with access to a
computer at home is high, but it probably isn't exactly 88% .
Copyright © 2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. A ndi Garing, Foundations of Statistics, 4th Edition
1. 3 Percentages and Proportions

Suppose we conducted a survey in our local neighbourhood and reported that only 70 of the
people interviewed supported the planting of more trees in the neighbourhood. How useful is
this piece of information? If you said "absolutely useless", you'd be absolutely right! Unless
you know how many people we interviewed, you don't have any useful information. If I
interviewed only 70 people then this represents 100% in favour of more tree planting, but if I
interviewed 1000 people, this represents a very low level of support.
This is where we need to present either the proportion, or the percentage, rather than the
actual number of people who support the proposal. You've probably calculated proportions
and percentages before, but just to refresh your memory:
Frequency
Proportion =
Total Number
So if 70 out of 1000 people supported tree planting, the proportion of people who support
more tree planting would be:
p roportwn = 70 = 0.07
1000
To get the percentage, just multiply this value by 100. In this case, the percentage of people in
favour of more tree planting was .07 x 100, that is, 7%. (We don't really require much more
mathematical skill in this text, so if you can calculate percentages your maths skills are fine!)
Proportions and percentages give you the same information, but in reports percentages roll off
the tongue more easily; "The proportion of respondents who support the proposal is only .07"
doesn't sound as good as "Only 7% of respondents support the proposal".
Let's look at another couple of examples where percentages are more useful than just the
number of cases. Consider the following excerpt from an article titled "Everyone enjoying
,,6
boom times: Costello
"More people were in work than ever before in Australian history and there were two
million more jobs than a decade ago, Mr Costello told ABC Radio."
Two million more jobs sounds like a lot, but how does this compare to the increase in the
number of adult Australians over that time? We might prefer to know how the proportion of
people in full time employment has changed over that period. (We might also have other
questions about those 2 million jobs: were they all full time jobs or were some of them part
time?)
Here's another example, this one comes from the intemet7, and looks at the number of
industrial accidents reported (I can't tell you what country the figures refer to - there was no
indication on the website of the source of these figures!) In 2005 there were 1300 industrial
accidents reported in the ' construction'industry but only 456 accidents reported in the
'shipbuilding and ship repair'industry. Does this tell us that it's more dangerous to work in
construction than in ship building? Not really- it depends on how many workers there are in
节： //www.thea e.com.au/news/NATIONAL/Eve one-en·o· -boom-times-

Costello/2007/02/ 13/1171128940734.html accessed 18/2/07
htt ://www.mom. ov.s / ublish/etc/medialib/mom libra /Work lace Safet /files6.Par.67751.File.tm /Numbe
roflndustrialAccidentsbylndustry19962005.pdf accessed 25/2/07
7
Copyright©2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. Andi Garing, Foundations of Statistics, 4th Edition
each of these industries. If there are far more workers in the construction industry, then we 'd
expect far more industrial accidents in that industry. If we want to make an informed
comparison, we need to know what percentage of workers in each industry are involved in
industrial accidents.
While we often need to know the percentage rather than the number of cases, there are some
situations where it's the actual number that is more important. To take a trivial example, if I
invite 50 people to my birthday party, I want to know how many are going to come, not what
percentage of those I invited are coming. If we go back to our original example about access
to computers at home - when I'm trying to estimate how many copies of the SPSS software I
need to order, I need to know how many students in my subject have access to a computer at
home, not what percentage.
屯 EXERCISE 1.5 (Solution on page 256)

a. In a random sample of 70 shoppers in a supermarket, 60 agreed that they would rather
be doing something else. What is the percentage of the shoppers in this sample who
would prefer to be doing something else?
b. Twenty people attended a training session. After the session they were asked to
evaluate the usefulness of the training. Six attendees described the training as
"helpful". What proportion of attendees thought the training was helpful?
c. Only 15 of the 20 students emolled in a tutorial came to the tutorial in the first week.
What proportion of the students emolled in the tutorial attended?
d. Of the 60,000 people attending a football match, 43,000 were wearing their club
colours. What percentage of those attending the match were wearing their club
colours?

a. In a study of high school students, 73 of the students interviewed had experienced
bullying over the internet. What further information would we need in order to draw
any useful conclusions?
b. A newspaper reported that 13 drivers pulled over by the police on the previous night
were "over the legal limit". What further information would you like to have?
岛 EXERCISE 1.7 (Solution on page 256)

A local council receives an application for a commercial development in a quiet Melbourne
suburb. They want to estimate the proportion of local residents who will be opposed to the
development. Thirty of the local residents are randomly selected and asked "Do you think
this inappropriate commercial development should go ahead?" (Note: If the sample is
properly selected, 30 is a reasonable size sample for this study.)
a. What is the population the local council is interested in?
A. All people opposed to the development
B. All 30 people who were interviewed
C. All local residents
D. All residents of Melbourne suburbs
b. The information collected from this sample is
A. Probably biased
B. Probably unbiased
c. Of the 30 respondents, 26 say that they are opposed to the development. What
proportion of these respondents oppose the development? Give your answer to 2
decimal places e.g. .34
d. What can we conclude from this sample statistic?
A. We cannot say anything about the proportion of local residents who oppose the
development
B. The proportion of local residents who oppose the development is the proportion I
calculated
C. A high proportion of local residents oppose the development, but it may not be
exactly the proportion I calculated.

A local council receives an application for a commercial development in a quiet
Melbourne suburb. They want to estimate the proportion of local residents who will be
opposed to the development. Thirty of the local residents are randomly selected and asked
"Do you support or oppose the application for this commercial development?" (Note: If the
sample is properly selected, 30 is a reasonable size sample for this study.)
a. The information collected from this sample is:
A. Probably biased
B. Probably unbiased
b. Twenty five of the 30 people interviewed say that they are opposed to the
development. What proportion of these respondents oppose the development? Give
your answer to 2 decimal places e.g.. 34
c. What can we conclude from this sample statistic?
A. We cannot say anything about the proportion of local residents who oppose the
development
B. 83% oflocal residents oppose the development
C. A high percentage of local residents oppose the development, but it may not be
exactly 83%
Module 1: Critical Thinking in Statistics
1 . 4 Summarising Data
Suppose a reporter wanted to write a report in their magazine about how much time
Australians spend doing housework. They might start by collecting a lot of information from
a carefully selected sample of Australian adults, but how would they present this information?
It certainly wouldn't make much sense to the readers if they just printed all of the raw data
they'd collected without analysing it in some way. We need some tools for summarising
information. Some of these tools, like percentages and the mean (average) you've no doubt
met before, but some, like percentiles and boxplots you may not have seen.
Some Tools
SPSS
Instead of slogging through lots of tedious calculations on a calculator, and drawing graphs by
hand (I was always hopeless at drawing graphs!) we'll get SPSS to do the analysis for us. In
the SPSS data file What_Analysis.sav, we have some relevant data about the lives of
Australian adults - including information on hours of housework - which is based on data
gathered in a government survey. Here's a view of the first part of the data file:
, sex a~e marital I hrstv ~ ethnic educlrs I occst I hr

1 』 I
11 。 20 5 2.
2 1 50 1
3 。 45 2 2.0 2 16 2
4 38 3 4.5 1 12 3
5 1 19 5 3.5 3 11
6 1 27 2.0 1 11
7 1 46 1 3.5 1 9
8 23 5 4.5 2 12
9 1 40 1 3.0 3
10 1 41 1 2.0 1 7
11 11 仁1 勹仁 1 7 亭
You can see that instead of recording'Male'and 'Female'for sex, number codes have been
used. This is a very common practice. Before we can interpret this information, we need to
know what each of the number codes represents. In this case, sex has been coded female = 0,
male = 1. This was a totally arbitrary choice, we could have used male = 1, female = 2, or
even male = 21, female = 37 ifwe wanted to, but it's best to keep the codes simple!
10
This coding is recorded as part of the SPSS data file. If we wanted to know what'marital'
represented, and how it was coded, we could just click on 斗圃 in the icon bar and select
'marital'in the list of variables:
Variables
Variable Information:
identification nu... 1.. marital
sex[sex) Label: Marital status
# age in years [age) Type: F5
l.larital status [... Missing Values: 9
, - 『-.一
# hours spent wat.. Measurement Level: Nominal

Value Labels:
1 married
2 separated
3 divorced
4 widowed
一、
worksituation la... I 11 115 never married
~旦respondent mco... 1 ..-
巨呜邑丘
Once again, the choice of codes was totally arbitrary!
So how do we go about summarising the information in this data file? We need a few
statistical tools.
Output from the FREQUENCIES procedure - Frequency Tables

To begin with, let's look at sex. We can get SPSS to produce a frequency table for this
variable (see Appendix A2, page 223, for details of how to produce each of the outputs
discussed in this section):
sex
Cumulative
Percent
Valid female 55.4
male 100.0
Total
Of the 444 people in the study, 55.4% were female.
11
Let's also look at the frequency table for marital status:

Marital status
Valid Cumulative
Frequency Percent Percent Percent
Valid married 281 63.3 67.5 ~ 67.5
separated 14 3.2 3.4 70.9
divorced 18 4.1 4.3 75.2
widowed 28 6.3 6.7 82.0
never married 75 16.9 18.0 100.0
Total 93.7 100.0
Missing 9 \ 4:: 6.3
Total 100.0
The frequency table tells us at percentage of people were in each catego . But there are two
columns in the table givin~ ercentages - one headed'Percent'anf ne headed'Valid
Percent'. Which one should w use? In most cases it's the'Valid Percent'that we're interested
in. This tells us that of the 416 people who answered the question, 67.5% said they were
married.
Output from the FREQUENCIES procedure - Pie Charts and Bar Charts
As well as the frequency table for these two variables, we might also want some sort of
graphical representation. So first let's look at Pie Charts.
sex Marital status

· 如~
m血
. • m:,mcd
口之立
口 d....:仄心
. w,cb八
口～心r mom<ld
Figure 1.2. Pie chart for sex. Figure 1.3: Pie chart fo r marital status.
From the pie chart for sex (Figure 1.2) we can see at a glance that there were more females in
the study than males. This gives a quick instant picture of the distribution. But the pie chart
for marital status (Figure 1.3) is not quite so useful. It's a bit too cluttered, and doesn't give a
nice clear picture of what's happening.1 When there are more than two or three categories, pie
charts are not very effective. There is an alternative whic~gives a much clearer picture of the
distribution when there are more than 2 or three categon es. This alternative is a percentage
bar chart. In a bar chart, each category in the variable is represented in a separate column, and
the height of the column represents the percentage of responses in that category. The
percentage bar chart for marital status is displayed in Figure 1.4.
1 Note that the pie chart produced by SPSS version 20 includes the 'missing values'category, and the
percentages shown would not the 'valid percentage'. We would have to edit the pie chart to remove the missing
value segment. Instructions for doing this are included in Appendix A2. In SPSS version 23 the missing value
segment is not included in pie charts.
12
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Marital status
From the bar chart, it's obvious that
60 the most common marital status was
'married'. (In statistics, this is called
芒只》』
4 the mode.)
。
<Id
In a bar chart, if there are no responses

20
for a category, that category doesn't
show on the bar chart. So, for example,
。
married separated divorced widowed never

if no one in our sample said they were
married
widowed, the barchart would only
Marital status
have four columns — widowed
Figure 1.4: Percentage bar chart for marital status. wouldn't appear on the graph.

a. Use the SPSS FREQUENCIES procedure to produce a frequency table and a
percentage bar chart for occupation. (Data in What_Analysis.sav.)
b. What's the most'typical'occupation in this sample? Is this easier to see from the bar
cha门； or the frequency table?
c. Of the people in this sample who gave their occupation, what percentage were semi-
professional/managerial?
d. Now use the FREQUENCIES procedure to produce a pie chart for occupation. Do you
think the pie chart or the bar chart gives a clearer picture of the distribution of
occupation?

a. Produce a frequency table, a percentage bar chart, and a pie chart for'work situation
last week'. The data is in What_Analysis.sav. (You'll have to run the
FREQUENCIES procedure twice- once for each chart.)
b. What's the most'typical'work situation in this sample? Which part of the output did
you use to answer this?
c. Of the people who responded to this question, what percentage were working full
time? Give your answer correct to one decimal place.
d. Which graph do you think is more useful here, the bar chart or the pie chart?

The Beneffi Wellness Centre offers three different types of massage: relaxation, pregnancy
and remedial. Over the course of a week they record the number of clients booking in for
each type of massage. The information is recorded in the massage.sav data file.
a. Produce a frequency table and a percentage bar chart for type of massage.
b. What was the most common type of massage at the Beneffi Wellness centre?
c. What percentage of clients booked in for a remedial massage.
d. Explain why the "Percent" and the "Valid Percent" columns are identical in this
frequency table.
13
Copyright©2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. Andi Garing, Foundations of Statistics, 4th Edition
Output from the EXPLORE procedure - Histograms

Now let's have a look at the distribution of time spent watching TV (hours/day). For this
variable we'll use a different graph, called a histogram. (Instructions for producing and
modifying histograms are given in Appendix A3, page 226.)
HistoQr am
0 1 23 4 56789
hours spent w忒ching TV each d ay
Figure 1.5: Distribution of time spent watching TV.1
Histograms look similar to bar charts, but there are some really important differences. In a bar
chart, each bar represents one category, and each bar is labelled individually. With a
histogram, what we're doing is grouping the data. Note that each of the columns in the
histogram has the same width. So the first column in the histogram tells us how many people
watched from O up to but not including 1 hour of television each day (about 8), and the
second column tells us that about 20 people watched between 1 and 2 hours per day (up to but
not including 2 hours) etc. Looking at this histogram we can see that most people watched
between about 2 to 6 hours per day. Histograms don't give us very specific information about
what's'typical'. We'll g et much more detailed infom画on when we look at some summary
statistics.
Histograms give a very good overall impression of the shape of the distribution. You can see
that there's one central peak and the hours of TV are fairly evenly spread on each side of this
peak. We say the distribution is approximately symmetric. Distributions can have all sorts of
different shapes:
40 The histogram in Figure 1.6 represents the level

3020 of anxiety recorded for a sample of students just
A:iua』
before they were about to sit an exam. This

distribution has two peaks; we call it'bimodal'.
n
Lb
There were a lot of students with quite low levels

La
10
of anxiety, but there was another large group of
。 students with high levels of anxiety.
0 10 20 30 40 50 60
Anxiety before exam

Figure 1.6: Bimodal histogram.
1 Note that the histogram in Figure 1.5 has been modified to have an interval width of 1 and an 'anchor'ofO.
14
Copyright © 2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (978148861 3432), Dr. Andi Garing, Foundations of Statistics, 4th Edition
125 The histogram in Figure 1. 7 shows the distribution

>, 100 of'level of enthusiasm for statistics'. You can see
l
巴
75
50
that the bulk of students had high levels of
enthusiasm, but the tail of the distribution drags out
u.
25 to the left with a few students having extremely low
。 levels of enthusiasm. We call this'negatively
10 20 30 40 50 skewed'.
Enthusiasm for Statistics
Figure 1.7: Negatively skewed histogram.
2500
The histogram in Figure 1.8 represents house prices,
K3C
anbaJ:l75
in thousands of dollars. The tail end drags off to the
right, with a few unusually high values (outliers).
50250
We call this'positively skewed'.
400 600 800 1000

House prices in $'000
Figure 1.8: Positively skewed histogram.
Let's look at just one more. Using the data in the What_Analysis.sav data file, produce a
histogram for the variable'Time to travel to work (minutes)'. SPSS produces the histogram in
Figure 1.9.
25
20
AouanbaJ:l
1510 Note that the distribution is approximately
symmetric
50
10 15 20 25 30
Time to travel to 叩rk (Minutes)
Figure 1.9: Distribution of travel times.
40
If you are not using Version 23 of SPSS you 302010
,<;::,uanbaJ.::t
may get a somewhat different looking
histogram for this distribution, like the one in
Figure 1.10. This histogram looks like it has
three peaks. However, this is just a result of the
inappropriate way SPSS has grouped the values
。
together into the columns. If you changed the

column width to 1, the histogram will look like 10 15 20 25 30 35
that in Figure 1.9. Instructions for changing the Time to travel to work
column width are given in Appendix A3 (Minutes)
(page 226). As a general rule, always check that Figure 1. 10: Histogram for travel times
the column width is a whole number. produced in earlier SPSS
versions
15
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Describe the shape of each of the following distributions
40
8 20
505
11
否 U$beLL
3020 64
A:luan
A:iuanbw:1
』
LbLa
2
10
。
。
。
10 20 30 40 50 60 4.0 4.5 5.0 5.5 6.0 6.5 7 .0 30 40 50 60 70 80 90
Feeling of well being ENERGY/ENTHUSIASM marks

Compare the bar chart and the histogram for'Number of basketball matches attended'
shown below. How do the two graphs differ? Which gives a clearer impression of the
distribution of number of matches attended?
25201510
20
5 11
505
芒
uanbaJ:t
33』
8d
50
。
5 10 15 20 0 11 12 13 14 15 16 17 18 19 20
Number of basketball matches Number of basketball matches
attended last year attended last year
Histogram Bar Chart
Output from the EXPLORE procedure - Summary Statistics

Histograms give a detailed visual representation of distributions, but sometimes it's helpful to
be able to summarise this information. For example, consider the distribution of time taken to
get to work shown in Figure 1.9. We'd like to be able to give people a quick idea of typical
travel times. It's very tempting to just pick out the tallest column in the histogram and say
that's the most common time. So in this case, if you look closely at the histogram, you'll see
that the tallest column is the one centred at 17 minutes. We could report that the most
common time taken to travel to work is from 16.5 to 17.5 minutes - but does this really look
like the centre of the distribution? - no - it looks a bit too low. In fact, if you look at the
histogram for the same data, shown in Figure 1. 10, you'd have come up with a different
'typical value' - you would have said that the most common travel time was from 20 to 21 ¼
minutes. Just changing the way the values are grouped together into the columns can
drastically change the'modal class'. Giving the modal class is a very unreliable way of
measuring what's'typical'- that is, of measuring where the distribution is centred.
16
Copyright©2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. AndiGaring, Foundations of Statistics, 4th Edition
There is a much more reliable way of indicating what the typical travel time is. You've
probably met it before - the mean. To calculate the mean, you just add up all of the values and
divide by how many cases you had. So, for example, suppose I asked 5 people how long they
took to travel to work, and their answers were: 18 min, 20 min, 22 min, 20 min and 20 min.
Then the mean would be :
18 + 20 + 22 + 20 + 20 100
Mean= =— = 20
5 5
So in this small sample the average time taken to travel to work was 20 minutes. This is easy
when you have just 5 cases, but it can be pretty tedious if you are dealing with hundreds of
cases. Fortunately for us, we don't need to do any calculations by hand at all —SPSS will do
all of the calculating for us. Part of the output we get from the EXPLORE procedure (see
Appendix A3, page 226) is a table of summary statistics:
Descriptives
Std.
Statistic Error
Time to travel to Mean 19.98 .318
work (Minutes)
95% Confidence Lower Bound 19.35
Interval for Mean
Upper Bound 20.61
5% Trimmed Mean 19.94
Median 20.00
Variance 25.249
std. Deviation 5.025
Minimum 8
Maximum 33
Range 25
Interquartile Range 7
Skewness .102 I I .154
Kurtosis -.259 .307
For the moment we're only interested i a few of these statistics, and I'磷highlighted them in
the table. In this sample, the aver~ e taken to get to work was 19 .98 minutes. There is
another statistic here which weals ells us what's'typical' —the median. The median tells us
that half of the respondents spent 20 minutes or less travelling to work1. In this case the mean
and the median are very similar. This is because the distribution is symmetric.
So we've got a couple of statistics that tell us where the distribution is centred, but we might
also like some infom画 on about how spread out the travel times are. The simplest thing to
look at here would be the smallest and largest values. These are given as the minimum and
maximum in our table of descriptive statistics. The people in this sample took between 8
minutes and 33 minutes to travel to work each day.
芦 statistic for measuring spread, called the variance, and a related
statistic, called the standard eviation. The variance takes into account all of the data, not just
the two end points. It measures how much the values vary about the mean.
1 To calculate the median by hand you would start by writing the values in order from lowest to highest. The
median is then the middle value. So in the example with 5 cases given above, the values ordered from lowest to
highest are: 18, 20, 20, 20, 22. The median is 20; the middle value. If there are an even number of cases, then the
median is half way between the two middle values.
17
Copyright ©2016 Pearson Australia (a division of Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. AndiGaring, Foundations of Statistics, 4th Edition
For the mathematically minded, here's how it's calculated for the small sample of 5 cases we
had before. You won't need to calculate the variance by hand (that's what SPSS is for!) but
seeing how it's calculated can help you to understand what it's measuring.
Travel time Difference between travel

time and the mean, squared
(1) 忙汀凶T- 汀 8
Vanance
. = =— =2
18 (18-20)2=4 n —1 4
20 (20-20)2 = 0
22 (22 —20)2=4 Tue~symbol used here means
20 (20-20)2 = 0 'sum'or'add up'
20 (20-20)2 = 0
Standard Deviation=~Variance
8
So the variance is calculated by looking at how much each individual score differs from the
mean; squaring those differences, and averaging them. Basically it's a measure of how much
the scores vary about the mean. The descriptive statistics table gives both the variance, and
the standard deviation. The bigger the standard deviation (or the variance) the more spread out
the distribution. In our travel time example, the standard deviation, given in the Descriptives
table, is 5.028.

From the following SPSS output, give the mean and standard deviation for the test marks.
What is the lowest mark recorded in this sample?
Descriptives
Statistic Std. Error
marks Mean 63.34 1.144
95% Confidence Lower Bound 61 .07
Interval for Mean Upper Bound 65.61
5%Trimmed Mean 63.32
Median 63.00
Variance 126.956
Std. Deviation 11 .267
Minimum 36
Maximum 90
Range 54

Use SPSS to find the mean and standard deviation for age and time to travel to work. The
data is in the What_Analysis.sav data file.
18
Copyright ©2016 Pearson Australia (a divisionof Pearson Australia Group Pty Ltd) ISBN (9781488613432), Dr. AndiGaring, Foundations of Statistics, 4th Edition
Output from the EXPLORE procedure - Percentiles and Boxplots

The EXPLORE procedure also gives us some other useful statistics - percentiles.
Percentiles
Percentiles
5 10 25 so 75 90 95
W(DeeifginhtiteiodnAverage Time to travel to work 11 .55 13.00 17.00 20.00 24.00 26.00 29.
1) (Minutes) \
Tukey's Hinges Time totravel to work 17.00 20.00 24.00
(Minutes) \ 、｀
How do we interpret these percentiles? Start with the 10th percentile, 13 minutes. This tells us
that only 10% of the people in our sample took 13 minutes or less to travel to work. The 25th
percentile tells us that 25% of the people in our sample took 17 minutes or less to travel to
work, and so on. So the median, which we introduced earlier, is the 50th percentile.
There's a bit more new terminology to learn here. The 25th percentile is also referred to as the
first'quartile ' and the 75 th percentile is also called the third quartile - one quarter of the
scores are lower than the first quartile and three quarters of the scores are lower than the third
quartile.
Percentiles are very useful for placing an individual case within a distribution. So, for
example, if your travel time was at the 90th percentile, it would indicate that relative to other
people you took a long time to get to work. In fact, only 10% of people took longer than you
did.
Using percentiles can also help us to summarise the distribution - which leads us to our last
graph - the boxplot. Boxplots give a "5 number summary" of the distribution. They display
the minimum, first quartile, median, third quartile and maximum. The boxplot for travel times
is given in Figure 1.11.
35
30
25
——
24 min. ,~ —
,,
20 min.
20 Il一·—
~
l
17 min.
15
~ —·
10
5
Time totravel to work
(Minutes)
Figure 1. 11: Boxplot for travel times.
The numbers down the left hand side of the boxplot are travel times. The boxplot tells us at a
glance, that 50% of people in the sample took 20 minutes or less to travel to work, and the
middle 50% of travel times were between about 17 and 24 minutes. This gives us a feel for
both what is typical and for how variable travel times are. Boxplots don't contain as much
detail about the shape of the distribution as histograms, but they're really useful when you
want to compare several distributions.
19
Copyright©2016 PearsonAustralia (a divisionof Pearson Australi a GroupPtyLtd) ISBN (9781488613432), Dr. AndiGaring, Foundations of Statistics, 4thEdition
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several thousands every year, but in 1902 they sank to the
comparatively small total of 600. But whilst every endeavour is made
to govern the country on lines acceptable to and understood by the
people, there are, of course, some points on which the policy of a
civilized government is necessarily in opposition to very deep-rooted
customs and habits to such a degree as to completely upset the old
basis of social life. In a minor degree this is true of the partial
application of the game laws to natives, but of far greater importance
is our attitude towards the institution of slavery and the slave-trade.
The occupation of the Soudan has been a tremendous blow to
slavery; one of the principal recruiting-grounds for slaves has
practically been closed. A certain amount of slave-raiding goes on
along the Abyssinian frontier. Descents are periodically made by
parties one to two hundred strong, well armed, from the south-
western districts of Abyssinia. They raid the Barun negroes, and
carry off the women and children. The same kind of thing is apt to
happen on the Darfur frontier, and some of the remote tribes in the
same quarter sometimes raid each other with the object of getting
slaves. Some of these, but not many, find their way to Dongola, or
the Ghezireh; others are taken to Tripoli. Special steps have now
been taken by the Anti-Slavery Department of the Egyptian
Government, which now has its headquarters at Khartoum, to put
down this traffic. Two extra English inspectors have been posted,
one at Rosaires, on the Blue Nile, the other at El Obeid. They are to
form small mounted corps of the best Arabs and patrol the disturbed
districts.
Apart from the actual work done, it will be a great thing to enlist
the best of the Arab tribesmen in the Government service, and it is
hoped that they will in time form the nucleus of an effective native
police. These men have been in the past some of the principal
exponents of slave-catching themselves; they ought to be very adept
at their new business. With these exceptions the slave-trade within
the borders of the Soudan has practically disappeared. During the
first year or two captures were occasionally made of small caravans,
but very heavy penalties were imposed. There is still a constant
demand for slaves in Arabia, and once a slave is shipped over the
Red Sea a good profit is assured. But it is too dangerous now for
anyone to try to make a regular livelihood by it. There are still,
however, about twenty cases a year of trials for offences against the
slavery laws, mostly isolated cases of kidnapping a woman or a
child, and probably there is besides a fair proportion of undetected
cases. But the regular trade is pretty well stamped out.
The benefits of the abolition of slave-raiding and kidnapping are
immediate and obvious to everyone. Even the Arab can understand
them, but he finds it very difficult to appreciate our attitude—which,
needless to say, is uncompromising enough—towards slavery as a
domestic institution. It is the one serious complaint which he has
against the new government. His domestic habits and customs have
been completely based on slavery for centuries. Slavery is permitted
and recognised by the Koran. In most cases the slaves themselves
have been treated more like members of the family than as slaves,
and no doubt many of them have had far happier lives than they
would have had in their own villages. Nor is it difficult to point to evils
which have arisen from the emancipation of the slaves. It is a
melancholy fact that many of the towns in the Soudan are crowded
with freed slaves, too lazy to do anything but steal, while the women
have recourse to an even less reputable occupation. It is easier to
break down the social system of centuries than to build up a sounder
fabric in its place. But the thing had absolutely to be done if the
Soudan was to have a real regeneration. Even when the slaves have
been well treated, the demoralization caused by slavery has been
great. The Arabs have all the vices of a slave-owning people. It was
a good time to make an absolutely fresh start. All changes of such
magnitude are bound to produce dislocations. The evils of the
change will die out with the present generation. The good must be
waited for patiently, but it is sure to come.
CHAPTER XIX
EDUCATION AND THE GORDON COLLEGE
Probably the last thing that a military government might be

expected to take an interest in is education, and yet few educational
establishments are so widely famous as the Gordon College at
Khartoum. As yet it owes its reputation to the fact that it was founded
by one great soldier in memory of another, not to its achievements; it
was born great. But already it has justified its founders; its mere
existence marks an extraordinary contrast between the character of
the present régime in the Soudan and that of any preceding.
Whenever the Soudan is mentioned, the first question asked is,
‘How is the Gordon College getting on?’ and the question cannot be
answered in a word. The actual building is indeed for the present
complete. It is a handsome structure of native red brick, built in the
Moorish style, but retaining the collegiate character. It occupies two
sides of a square, the front facing on the river. In the centre is the
principal entrance, and over it a tower. If the original design is finally
carried out, the whole quadrangle will be completed. Along the inside
runs a cool and airy cloister, with winding stairs leading to the upper
story; the class-rooms are spaciously designed. Its commanding
position at the east end of the town makes it a conspicuous
landmark for many miles round. From no point is this so remarkable
as from the hill of Surgham, which overlooks the battlefield of Kerreri.
Here is summed up much of the past and the future of the Soudan.
On the one hand is the scene of the final overthrow of the forces of
darkness and ignorance by war; on the other the symbols of that
longer contest for the conquest of the Soudan by the peaceful arts of
science and learning.
With the eye of faith it is easy to look forward into the future, and
to imagine the time, generations hence, when the Gordon College
will be a true centre of learning for all these vast territories. Then it
will stand, a completed quadrangle, in the middle of large gardens,
its own territory, as green and cultivated as they are now arid and
dusty. Its halls and class-rooms will be crowded with picked students
from all the provincial centres, not vainly pursuing a dry and vain
scholasticism, as in the other degenerate Universities of the
Mohammedan East, but eagerly following in the paths of living
science, and learning by practical teaching in the laboratory and
workshop to wrest from Nature her secrets, and to absorb the
principles underlying practice in the departments of chemistry and
medicine, mechanics, agriculture, and the arts. Perhaps once more,
in years to come, the culture and science of the Arabs will be as
famous as they were in the great days of Arab dominion.
It is a long way to travel from such stimulating forecasts to the
actual state of learning and education in the Soudan to-day. There
was not much learning under the Egyptians, but at least a certain
amount of theological study went on. Under the Khalifa even that
was sedulously discouraged, and the books were ordered to be
destroyed because he feared that they might tend to discredit the
unorthodox doctrine of Mahdism. Reading and writing were not likely
to flourish under a ruler who, possessing neither of these arts
himself, and entertaining strong suspicions of those who did, was
wont to give drastic expression to his views. As a consequence,
there never was a country more absolutely and wholly illiterate.
Writing is practically an unknown art, and reading hardly less so. It is
perfectly useless to post a Government Proclamation unless a
competent person is stationed by it to read it out to any passer-by. At
the same time, there flourishes the most exaggerated respect for a
written document, which is regarded as a kind of magic book, and
cases have been known in which swindlers have extorted large
sums of money by going round exhibiting a paper professing to be
an order to pay issued by the Government. Obviously, education has
had to be on very humble lines at first, and must continue so for
some time.
Was, then, the Gordon College a too ambitious attempt to
anticipate the future? Is it a mere white elephant, doomed to be a
vain monument of an ill-directed wave of enthusiasm? Such a view is
far from the truth. It would be strange indeed if a project so dear to
the heart of Lord Kitchener was of such a nature. Certainly, it is
impossible to start a complete University right away with a building
and an endowment of some £4,000 a year. Time is of the essence of
the question. It is possible to argue that the money used in the
building might have been more advantageously expended in other
ways. But, apart from the fact that the subscribers doubtless wished
to see some immediate result for their munificence, I am sure that it
was the right policy to build at once.
For the Gordon College, though not yet a University, is much
more than a college. It is the centre of all the new educational and
intellectual influences in the Soudan. Its director is also head of the
Education Department; the activities of both are inseparably
connected. It acts as an extraordinary stimulus upon the authorities
in the direction of education. It would have been so easy and so
natural for a Government so hard beset for money to neglect
education for other objects, apparently more practical and more
immediately pressing. The actual material presence of the college
makes it impossible for its claims to be overlooked. Very likely
without it there would not have been an Education Department at all.
Secondly, but for the existence of the building, the Soudan would
certainly never have obtained such valuable gifts as those of Mr.
Wellcome’s bacteriological laboratory and Sir W. Mather’s complete
technical workshop apparatus, containing all that is necessary for the
establishment and organization of departments for manual training
and technical instruction. Thirdly, the building itself has been already,
and will be to an increasing extent, of the greatest use; and,
moreover, there is still about £100,000 of the original endowment
remaining, the income from which is playing a great part, as will be
shown, in providing the beginnings of education in the Soudan, and
so laying the foundations for the future work of the college itself. Lord
Kitchener was wiser than his critics. Among his many claims to fame,
none is greater than the clearness with which he saw that a sound
educational system is one of the fundamental requirements of the
Soudan, as well as a substantial foundation for our rule.
In 1901 the Soudan Government spent £1,421 on education, in
addition to the Gordon College endowment; in 1902, £3,577; and in
1903 something over £6,000. With such resources as these, it is
obvious that nothing heroic could be attempted. Only the more
immediate needs could be attended to. Looking to the necessity for
the education of a class of native public servants, it was most
important to establish some sound primary schools, in which the
boys should be given a fair general education in reading, writing, and
arithmetic, besides a certain amount of history and geography and
English. Four of these schools are now in existence; two of them,
those at Halfa and Suakin, were established some eight or nine
years ago by the Egyptian Government, and have only recently been
handed over to the Soudan; they are in an efficient condition. The
most interesting, considering their recent establishment, are those at
Khartoum and Omdurman. That at Omdurman was the first, the
direct offspring of the Gordon College. It now numbers over 200
pupils, and is in a most flourishing condition. There are constant
applications for admission, partly, no doubt, from the reason that
pupils of the school are thought likely to obtain Government
employment, but partly also from a real appreciation of the
advantages of education.
The school course is divided into four years, and the curriculum is
based on the Egyptian one—modified to the extent that no subjects
are taught in English, except English itself. An inspection of the
school made it clear to me that, at any rate, in the subject which I
could understand—the teaching of English—the methods were
thoroughly sound, and the results good. Pupils in their last year are
also taught land-measuring. The reason is the great demand which
comes from every province for land-measurers—a most important
thing in view of the assessments for the land-tax—while no trained
men are available. This part of the work is taught both in the class-
room and practically in the field. I am certain that in a very short time
there will be land-measurers available of very good ability, so
excellent was the quality of some of the work done.
Some, of course, of these boys are the sons of Egyptians in the
Government service, to whom it is a great blessing to be able to get
a good education for their children on the spot. But far the majority of
them—at least 90 per cent.—are genuine Soudanese, some of them
members of good Arab families, whose fathers were prominent in the
service of the Khalifa. Originally it was intended that this school
should be transferred to Khartoum, and housed in the college as
soon as the general exodus took place. But as Omdurman shows no
signs at present of diminishing, and is, indeed, once more
increasing, the school has been kept on, and another started on
similar lines in Khartoum itself. This school is also flourishing, but it
naturally contains a larger proportion of the Egyptian-born pupils;
altogether it has about 120 scholars. This school is now housed in
the Gordon College itself.
Book-learning is not the only channel of instruction employed. I
had the good fortune to be umpire in the first football match between
Khartoum and Omdurman schools, in the mosque square at
Khartoum. It was a hot afternoon, and I felt as though I should get a
sunstroke whilst umpiring; but these boys, all hatless as they were,
played with great energy, and appeared to derive nothing but benefit
from the heat. They played a good game, and it was pleasant to see
that what they lacked in experience they made up in courage and
determination. All the players, of whatever shade of black or brown,
and the shades were very various, showed a spirit which augurs well
for the future. Anybody who can play football with energy in Central
Africa must have good stuff in him. The match was drawn.
In another direction also an encouraging start has been made.
There is at present in the Soudan no skilled native labour;
blacksmiths, tinsmiths, carpenters, and bricklayers, are all in
demand, and have to be imported from outside at great trouble and
expense. In the hope of meeting this demand, an industrial school
has been established at the Dockyard Works, which are now on the
river at Omdurman, but which will eventually be moved to Halfaya.
The head of the Steamboat Department agreed to take in sixty boys
as apprentices. These are divided into two shifts of thirty each, and
they alternately receive a day’s schooling and do a day’s practical
work at their separate trades as carpenters, fitters, or riveters. In
school their time is divided between reading, writing, and arithmetic,
and also drawing. The plan has been found to answer admirably. Not
only does the education they receive improve their intelligence as
workers, but some of the boys have shown such proficiency in
drawing that they are able to copy engineering and building designs
with such accuracy as to be able to relieve the English
superintendents of a good deal of work. Many of these boys are
sons of men employed in unskilled labour at the works, who take the
greatest interest in seeing their sons advance so far beyond
themselves. Many applications for admission have to be refused,
and there is little doubt that when Sir W. Mather’s technical school at
the Gordon College is in full swing, it will fill a great need in the
requirements of the country.
On the whole, the most difficult task which the Director of
Education has to face is that of diffusing the elements of knowledge
among the masses of the people. The great distances to be covered
alone impose a tremendous obstacle. But it is extremely important
that at least a portion of the population should be able to understand
the outlines of the machinery of government as laid down in notices
and proclamations, so as to be able to protect themselves against
the exactions of minor officials and the frauds and deceits practised
on them by wandering rogues. It has wisely been determined to
proceed along the lines laid down by Mohammedan tradition. The
kuttabs, or preliminary schools, are a well-known part of the ordinary
religious organization. They are supposed to give instruction in
reading and writing and the Koran, and there are many of them
scattered over the Soudan, as in other Mohammedan countries.
They are, in fact, a sort of private elementary school, something like
the old dames’ schools once existing in parts of England.
Unfortunately, they are almost entirely useless at present. The
teachers are incredibly ignorant. What little instruction they give is
confined to teaching by rote certain passages from the Koran, the
meaning of which is understood by neither pupil nor teacher. The
buildings are usually filthy to the last degree. The idea is to establish
model kuttabs in different parts of the Soudan, and to make them as
efficient as possible, so as to improve the others by their example.
To quote the words of the Director:
‘The process of formation has been in all cases the same. With the help of the
Mudir, a suitable building is put up; then the least incompetent sheikh that can be
procured is installed. After confidence has been established, and the nucleus of a
school formed, he is superseded by a trained teacher from Egypt, who, under the
local supervision of the Mudir and occasional supervision from my office, begins to
reduce chaos to order.’
Progress has not been very rapid. Lack of money and lack of
competent schoolmasters sadly hamper all operations. But kuttabs
are now established, attached as a sort of junior class to the schools
at Khartoum, Omdurman, Halfa, and Suakin. A model kuttab has
been established at Berber, which is reported to be doing well, and
another is being built at Dongola. The like is also being attempted at
Wad Medani, a populous town on the Blue Nile, capital of the
province of Sennar, with about 40,000 inhabitants. Reference has
been made to the lack of trained schoolmasters. Egypt itself feels
this difficulty, and Egypt is at present the only source of supply on
which the Soudan can draw. It was to meet this demand—at least,
so far as the kuttabs are concerned—that a small training college for
native sheikhs was opened in the beginning of 1901 in connection
with the school at Omdurman. At first this interesting experiment was
not very successful. The students, who all belonged to the best Arab
families, were all proud, ignorant, and lazy; and as Arabs they were
inclined to despise the Egyptian schoolmasters, whose task it was to
teach them. But now there is a great improvement. They have
increased in number to about thirty, and only lack of room prevents a
further increase. I watched them doing their own lessons, and also
receiving practical instruction in teaching by taking a class of the
school under the guidance of a master. It was impossible to doubt
the value of the experiments. They were nearly all fine-looking,
intelligent young men, some of them really handsome, with the keen,
clear-cut features that mark the pure-bred Arab. Three of them had
come from distant Kassala, where at present there are no means of
education whatever. The course lasts three years. At the end of it
they are to be examined as to their fitness, and they will then be
drafted off either to teach in their kuttabs or else to some posts in
connection with the native Courts. Whether as schoolmasters or
Cadis, they will be most useful elements in the development of the
Soudan.
In the negro portion of the Soudan, inhabited by the pagan tribes,
the people are so backward in civilization that the question of
education does not at present arise, or, if it does arise, assumes a
totally different aspect. Here is the field for the missionary. Two
missions are already established—one, the American Medical
Mission, on the Sobat; and the other, the Austrian Roman Catholic
Mission at Taufikieh, on the White Nile. Both are doing good work,
and both are to be encouraged and assisted by the Government. In
other parts of the Soudan it must be remembered that we are
dealing with a fanatically Mohammedan population, and any
suspicion that the Government was trying to proselytize would
immediately wreck all schemes of education, and probably be the
signal for grave disorders.
It will be a long time before the schools turn out sufficient pupils to
fill the Government Civil Service, and there does not seem to be any
danger of producing mere ‘babus,’ hanging about and relying on a
certain knowledge of English to procure them a job. The teaching of
English is entirely confined to those boys who are going to make use
of it in the Government Service or in commercial pursuits, where its
knowledge is required. For the ordinary mass of the population
nothing is to be gained by an imperfect knowledge of English. The
authorities are unquestionably right in discouraging such teaching;
the supposed political advantages of it are small, if not entirely
imaginary. The Soudan can never be a real white man’s country; its
rulers must always be speakers of Arabic, and its people will do far
better to employ their time in more useful ways than struggling with a
foreign language.
The Gordon College is the centre of education, but even now its
activities are not confined to mere teaching. It is proposed to form a
collection of books dealing with the Soudan, its peoples, its natural
history, and its various productions, accompanied by specimens to
illustrate them, and some progress has been made. Mr. Wellcome’s
valuable bacteriological research laboratory is in full working order,
and a skilled expert from Scotland has been in charge of it for some
months. He is doing a work of great importance, not only to the
Soudan, but also to the scientific world in general. The Soudan is a
land where strange diseases both of men and animals abound.
There is a wide field for research. The scientific and systematic
examination of these obscure subjects is already bearing fruit, and
cannot fail to ameliorate the conditions of life in these tropical
regions for the European as well as for the native.
Lord Cromer has promised that more shall be done for education
in the future. There is no need for hurry; indeed, it is essential that
the educational system shall be built up slowly with caution and
patience. But in time each province will have its own primary and
technical schools, whose pupils will be selected from the elementary
kuttabs. Afterwards, when all this has been carefully organized, the
provincial schools will in their turn pass on their more promising
students to Khartoum to receive the higher education which will then
be demanded. Then the Gordon College will at last become a real
college. In it the germ of a most hopeful future is contained. If the
work proceeds on the same sound lines as hitherto—which there is
no reason to doubt—great days are coming. The Arab is capable of
a very high degree of civilization, and has a great intelligence, which
has as yet had no chance of development. And in those days, I
doubt not, those who founded the Gordon College, and first kindled
the fire of learning, will be praised by its students as sincerely and as
deservedly as the benefactors of any of our own Western
foundations.
CHAPTER XX
TRADE AND COMMERCE
Sir Rudolf von Slatin, Inspector-General of the Soudan, who

possesses an unrivalled experience of the country, reports that ‘the
whole situation in the country is very satisfactory. Everywhere I went,
from north to south and from east to west, I found that villages and
cultivation had increased. The population is larger and wealthier;
flocks and herds are more numerous; security prevails, and general
satisfaction is expressed with the present rule.’ Once more, or,
rather, nearly for the first time, life and property are safe. Relieved
from the scourge of war and tyranny, people are everywhere
resuming their old occupations. They have even recovered from the
shock of finding themselves under just and settled government, and
are no longer content merely to exist. New wants are being felt, and
with the advance of material prosperity trade and commerce are
springing up.
There are, however, considerable obstacles to the development of
trade. First of all there is a lack of labour. Partly this is due to lack of
population, but partly also to other causes. Slavery has left its mark,
and many of the Arabs are too proud and too lazy to take part in
manual labour; in laziness, though not in pride, many of the negro
tribes are fully their equals. Secondly, there is the difficulty of
communications in so vast a country, and the lack of transport.
Thirdly, the Soudan is very poor, and capital is wanting. Still, every
year shows an improvement in these respects.
The population is steadily growing, partly by natural increase, and
partly by immigration from neighbouring countries of people who had
fled during the rebellion. Attempts have also been made to assist the
increase by colonization. A number of old soldiers from the
Soudanese battalions, who are enlisted for life, were permitted to
retire, and with their wives and children were established in villages
on the Nile and at Kassala. The villages were organized on a more
or less military basis, with a well-known non-commissioned officer as
chief. Each colonist was allotted two or three acres of good rain or
pasture land, or an acre of Nile foreshore. He was given grain for
sowing, besides a quantity of dhurra sufficient to support him until his
crops grew. Markets were also started. Unfortunately, the
experiments were generally unsuccessful. The colonies at Dongola
and Berber failed altogether. It was found that the black when
released from the strict discipline of the regiment was more anxious
to enjoy doing nothing, after the manner of his ancestors, than to
work, and if he saw a chance of living by begging or stealing he was
apt to leave his cultivation alone, and go off to some town.
At Hellet Abbas, on the White Nile, it was found that if the rains
were good the colonists would prepare the ground and sow the crop,
but if it came to artificial irrigation and shadoof work they soon tired
of this heavier labour and left the crops to wither. Happily, a much
better account comes from Kassala. The Mudir of that province
reported:
‘The colony of blacks established at Kassala continues to thrive, and in every

way justifies its existence. They have a well-laid-out village, and are eager to
cultivate along the Gash, and have also a fair amount of rain crops. Labourers can
nearly always be obtained from amongst them for public works, and there are
some very fair masons who are permanently employed. I wish we had the means
of teaching some of them carpentry and blacksmith’s work as well. They have
acquired a good deal of small stock.
‘Those of Gedaref are not so thrifty, and are lazy; they do not cultivate so much
or so well, but I hope for improvement.’
Transport and communications are indeed vastly better than they

were in Egyptian days. The railway from Halfa to Khartoum makes
an all-important difference. It has already given an immense stimulus
to the export trade; without it there would have been quite another
tale to tell of the last five years. But except in the province of Berber
it does not tap any local resources. Great part of it lies in an
uninhabited desert. Every train leaving Halfa has to carry with it
1,520 cubic feet of water. And there are 200 miles of river between
Halfa and the outer world at Assouan, and then 700 miles more to
the sea. Carriage of goods over such a mileage, with its necessary
transhipments, is a long and costly business, nearly prohibitive for
bulky articles. Coal, for example, is seldom less than £4 a ton at
Khartoum, and often nearer £6. No one who had to build a railway in
the Soudan for commercial purposes only would think of crossing the
desert to Halfa; his first thought would be to connect Khartoum with
the sea-board at Suakin.
There is also the railway from Halfa to Kerma, thirty miles from
Dongola. But this, too, was laid down in haste for military purposes.
It is laid so badly, with such sharp curves and such steep gradients,
owing to the nature of the country, that no heavy trains can run on it,
and with the present rolling-stock an engine has sometimes to make
three or four starts before it can master an ascent. It is worked at a
loss of about £20,000 a year, and it has become a serious problem
whether the money so spent could not be employed much more
advantageously elsewhere, so many are the claims on the Soudan
Exchequer. It would be far better to take up the whole line, and relay
it from Dongola to connect with the main-line at Abu Hamed. For not
only is this a much easier country, but the southern part of the
province, which is the richer, and inhabited by a more industrious
and hard-working population, would be opened up. But at present no
money is forthcoming either for this or for the complete repair of the
existing line. So poor Dongola is in the tantalizing position of having
a railway, and yet not being able to take full benefit of it. It is actually
suffering from a surplus of foodstuffs, and is a year behindhand in its
exports.
The province is famous for its dates; not only is it a great exporter
of the ordinary fruit, but it also produces a golden date, which is said
to be the best in the world, better, even, than the Algerine date, so
well known in Europe. It has also abundance of irrigable land as
good as Upper Egypt, which it very much resembles in general
climatic conditions. As its numerous and interesting antiquities show,
it once supported a very large population; but now a great deal of
land is lying waste, and the population, though increasing very fast,
is still not more than about 100,000. With better communications its
prospects are very good. When Egypt becomes overcrowded, as it
must in time if the present rate of increase is maintained, Dongola
will offer a fair field to Egyptian immigration. The conditions of life are
so similar to those in Egypt that it cannot fail to be the most attractive
part of the Soudan. Even as things are, owing to the partial
advantage afforded by the railway and facilities of transport by boat-
carriage on the Nile, the trade of the province is increasing. Cotton
goods and luxuries like tea, sugar, coffee, and perfumeries, are the
principal imports, and cereals are exported as well as dates. The
people are wealthier, and anxious to buy such goods as cutlery,
crockery, soap, agricultural implements, and hardware, but well-to-do
traders have not as yet exploited the field, as they would do if the
railway difficulty were solved.
Once Khartoum is connected with the sea by railway, the principal
obstacle in the way of trade will have been removed, and,
fortunately, this is no longer a mere vision of hopeful men. Practically
the railway has already been begun. It will strike across the desert to
the Atbara, crossing the mountains near Sinkat, and then run along it
to join the main-line near where it crosses that river. If the railway
does not come to Berber itself, Berber will probably travel up the Nile
to meet it. Arab towns are not very difficult to shift. The whole route
has been carefully surveyed, and a good deal has been spent in
improving the port of Suakin. Materials are being rapidly collected.
This time careful preparations are being made; there will be none of
those kaleidoscopic changes of policy which were so fatal in 1885. It
may confidently be expected that in two or three years’ time there
will be something to show very much more substantial than a tennis-
court at Dover built of much-travelled material, the only result of our
former exertions. For the construction of the line the Government will
be its own contractor. The Soudan Railway Department has a very
capable staff, and they will be able to do the work as efficiently as
any outside contractor, and much more cheaply. It is hoped that as
far as possible native labour may be made use of. It is a hopeful
indication of a change of spirit among the Arabs that the local
sheikhs have agreed to bring their tribesmen to work; the experiment
is worth trying even if it fails. No such thing has ever happened in the
Soudan before.
Meantime Suakin is looking eagerly forward. Its inhabitants have
naturally suffered by the complete diversion of trade to the Nile
Valley route. Very few of them can even afford to repair their houses,
and the town shows signs of decay. Most of the people are
unemployed, and labour is very cheap. There was formerly a good
deal of trade with India and the Red Sea ports, but most of this has
fallen away, and nearly all the Indian merchants who formerly had
their headquarters there have left. But now that the desert which
shuts off the Soudan from the sea is really to be bridged over, there
will be a great change. The one seaport of these immense territories
cannot fail to be a busy and prosperous place.
Once the new line is completed, the distance from Khartoum to
the sea will be reduced by about two-thirds, to some 450 miles, with
a proportionate reduction in expense of carriage, and it will then be
possible to think of building other feeder lines in various parts of the
Soudan. A branch line to Kassala and on to Gedaref and Gallabat
along the Abyssinian frontier will tap a very rich district and open up
the Abyssinian trade. Possibly in the distant future such a line may
be continued southwards so as to connect with Uganda. In the
recent agreement with Abyssinia, powers have been taken to build in
Abyssinian territory for this purpose. But this is still a long way
outside practical politics. Of far more importance for the immediate
development of the country would be a light railway from Omdurman
or Duem to El Obeid, or across the rich Ghezireh from Duem to Wad
Medani on the Blue Nile, or, again, from near Wad Medani to
Gedaref. Easy communication with the sea will render it possible to
bring the necessary plant into the country at a reasonable cost, and
the experience gained as to material and labour in building the
Suakin line will also be invaluable.
Meanwhile the provincial Governors are doing all they can to
improve the caravan routes and roads. In great part of the Soudan
this is simply a question of increasing the number of wells; metalled
roads are scarcely necessary as yet, outside a few towns. Wheel
traffic is almost non-existent; the camel and the ass are the great
public carriers. It is rather strange that the camel has not been more
used for pulling wheel transport than he has. One camel can pull
three or four times as much as he can carry. All the heavy machinery
of the Nile Valley Gold Mining Company, working in Nubia, has been
transported in this way from the river, a distance of sixty miles.
Rarely a camel may be seen hauling a plough in Egypt. But there are
limits to the use of camels. They cannot breed successfully south of
parallel 13°, and in all the country south of this the serut fly makes it
almost impossible for either them or horses to live at certain seasons
of the year.
Above all, access to the sea will greatly stimulate the use made of
water carriage within the country. In the Nile and its tributaries the
Soudan possesses a system of natural trade-routes unequalled in
Africa for internal commerce. The river traffic, though already
growing, is merely in its infancy. The Government has a considerable
fleet of steam and sailing vessels between Wadi Halfa and Assouan,
and also on the Blue and White Niles. They are also encouraging an
English company which has placed some steamers and steam-
barges on both rivers. On the Blue Nile there is regular steamer
communication with Rosaires, 426 miles from Khartoum, during high
Nile, about six months in the year, and even in low Nile most of the
river is navigable by native boats. On the White Nile, now that the
sudd has been cleared, steamers and native boats can ply the whole
year round up to Gondokoro. In time the Sobat may prove a very
good route for trade with Abyssinia. And the Bahr el Ghazal, with its
network of waters, is in this respect the most fortunate of all the
provinces. Many of its waterways are still blocked by sudd, but every
year the navigation is improving. A serviceable channel is now
available on the Jur River as far as Wau, and large steamers will
eventually be able to get up even much further than this. The other
rivers will in time be opened up. In a country where at present
everything has to be carried on men’s heads, this will be an
extraordinary benefit from every point of view, and if the province
answers at all to its old reputation as one of the most fertile spots of
Africa, it will do very well, in spite of mosquitoes, serut flies, malaria,
guinea worm, and all its other plagues.
As for the lack of capital both for private enterprise and public
works, that, like the lack of population, can only be cured by time.
Overhasty development could only do harm, even if it were possible.
As trade improves and agriculture develops, the people will become
more wealthy, and the two will react upon each other. That large
sums will be invested by private capitalists or firms is not to be
expected for years to come. But even now an Englishman is erecting
flour-mills at Wad Medani, and if his venture succeeds it may be
followed by others. The Government is doing all in its power to
encourage agriculture by small loans for the purchase of seeds,
water-wheels, and cattle to work them. Perhaps some form of State-
supported Agricultural Bank will be established.
The Soudan is an agricultural country; in that direction alone can
real progress be made, and the progress depends mainly upon
irrigation. Between the Atbara and the Blue Nile, and between the
Blue Nile and the White Nile, there is, as has been pointed out, a
great field for irrigation works on a large scale, but the amount of
crops now grown by direct irrigation is very small. Along the Blue
Nile water-wheels are numerous for the first ten miles above
Khartoum. There used to be 3,000 between Khartoum and Berber,
but in 1898 there were no more than seventy; and though the
number has increased, it has yet nothing like reached the old level.
The same is true of the rest of Berber Province and of Dongola.
There is also a certain amount of irrigation on islands in the White
Nile above Khartoum. When the river is falling, large mud flats
appear in the centre of the stream. To these the people transport
their cattle and belongings; they sow their seed in the mud, build
themselves huts, and set up shadoofs to water the growing crops of
wheat, barley, dhurra, and onions. They begin operations towards
the end of January, and in good soil the crops are harvested by May.
What perennial irrigation can do is shown by the gardens at
Khartoum, where lemons, figs, oranges, pomegranates, bananas,
vines, and all kinds of vegetables, grow in profusion all the year
round. But at present nearly all the crops are rain crops. The height
to which water has to be raised out of the Blue Nile is too great for
extended irrigation by mere lift. For the first 150 miles from Khartoum
the banks are 26 to 30 feet over the summer level, and further south
33 to 39 feet, the difference between summer and flood level being
about 23 feet. The soil of the Ghezireh is a rich alluvial deposit
sometimes 150 feet deep. The inhabitants build small dykes across
the general slope of the country so as to prevent the rain running off
too quickly, and sow their seed as soon as the rain has fallen. The
result as described by Sir R. Wingate a year or two ago is as follows:
‘I recently rode from Wad Medani on the Blue Nile to opposite Duem on the
White Nile, eighty miles across a perfectly flat plain sown almost throughout its
entire length with dhurra, which was standing 6 to 8 feet high. As there is only one
crop sown during the short rainy season, and as this is planted and harvested
within a period of sixty to eighty days, it follows that, if a system of irrigation were
possible in the Ghezireh it would become a huge granary capable of supplying, not
only the whole Soudan, but other countries as well.’
But, of course, any schemes for utilizing the waters of the Nile
have always to be considered in reference to the prior claims of
Egypt. It is only to Egypt that the Soudan can look for the money
necessary to carry out great works, and, naturally, Egypt would not
allow irrigation to be developed in the Soudan unless her own needs
were amply safeguarded. Whenever Egypt undertakes the great
works contemplated on the Upper Nile, the Soudan will share in the
benefit. That will not be for a long time to come, and meanwhile the
Soudan has opportunity to develop her resources and her population
so as to be able to seize the chance when it comes. There seems to
be no reason, however, why works on a small scale should not be
undertaken, subject always to the question of expense, to utilize in
the Soudan, by means of basin irrigation on the Blue Nile or the
Atbara, some of the flood-water during July, August and September,
which is only an embarrassment to Egypt now that perennial
irrigation is adopted so universally in that country. It is only in the
preceding summer months, when the Nile is low, that Egypt is forced
to watch the proceedings of her neighbour with such a jealous eye. It
would be rash to prophesy exactly when irrigation works will be
undertaken, or what form they will take; but it is certain that they will
come, and when they do, their effect upon the Soudan will be
immense. The subject is of peculiar interest to England; the lands in
question are capable of producing other crops than cereals, and, as
will presently be shown, for none are they more suitable than for
cotton.
Quite apart from any such speculations upon the future, the
external trade of the Soudan is capable of great expansion under
present conditions. An examination of the returns of imports and
exports during the last years before the rebellion is a very useful
guide to the capacities of the country. The figures are taken from
Colonel Stewart’s report.
There are no returns of imports except for the port of Suakin, but
these embrace practically the whole. Of course, a certain amount
came in by the Nile Valley route, just as now a certain amount comes
in by Suakin instead of by the railway. The position has been
practically reversed, and for purposes of comparison it is fair to take
the imports formerly entering the port of Suakin and those now
carried by the railway. The most important item was cotton goods,
which amounted to about 25,000 to 30,000 kantars annually. Linens
were about 200 to 300 kantars, and woollens 100 to 300 kantars.
There was also a certain amount of silks and silk thread and sewing
cotton. The Indian trade brought in a good deal of grain and tobacco.
In 1881 the import of Indian rice amounted to 20,000 kantars.
Petroleum (6,000 kantars), oil, zinc, copper, and iron, appear in the
list, as well as flour and provisions of various kinds in large
quantities, and candles, boots, and clothes. The peculiar tastes of
the Soudanese in luxuries are reflected in the large imports of
sandal-wood, and scents and perfumery, especially fish-scent (700
tons, or 15,400 kantars, a year). Both men and women are
particularly fond of strong, greasy scents. In all native festivities and
entertainments these scents are a very prominent feature, and a
native marriage can be smelt a very long way off. Last, but not least,
comes a very peculiar item: in one year no less than 11,000 dozen
umbrellas were imported. There is certainly enough sunshine in the
Soudan, and in parts of it rain also, to justify a large number of
umbrellas, but it is difficult to believe that 132,000 umbrellas would
find a ready sale in the Soudan to-day. Perhaps the Khalifa
particularly disliked the umbrella-carrying class.

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1. 1 Statistics in Everyday Life

Peter Lavelle published 29/05/2003, http://www.abc.net.au/health/library/stories/2003/05/29/1831797.htm

computer at home? • yes

Populations and Samples

~EXERCISE 1.1 (Solution on page 255)

~EXERCISE 1.2 (Solutiononpage255)

Other Sources of Bias

When you're looking at a statistical report in anything from a newspaper to a scholarly

1. How were the individuals or objects in the study selected?

2. Exactly what measurements were made or what questions asked?

~EXERCISE 1.4 (Solution on page 256)

Samples versus Populations

1. 3 Percentages and Proportions

节 ： //www.thea e.com.au/news/NATIONAL/Eve one-en·o· -boom-times-

屯 EXERCISE 1.5 (Solution on page 256)

屯 EXERCISE 1.6 (Solution on page 256)

岛 EXERCISE 1.7 (Solution on page 256)

屯 EXERCISE 1.8 (Solution on page 257)

, sex a~e marital I hrstv ~ ethnic educlrs I occst I hr

# hours spent wat.. Measurement Level: Nominal

Once again, the choice of codes was totally arbitrary!

Output from the FREQUENCIES procedure - Frequency Tables

Of the 444 people in the study, 55.4% were female.

Let's also look at the frequency table for marital status:

sex Marital status

In a bar chart, if there are no responses

married separated divorced widowed never

屯 EXERCISE 1.9 (Solution on page 257)

屯 EXERCISE 1.10 (Solution on page 258)

~EXERCISE 1.11 (Solution on page 258)

Output from the EXPLORE procedure - Histograms

hours spent w忒ching TV each d ay

Figure 1.5: Distribution of time spent watching TV.1

40 The histogram in Figure 1.6 represents the level

before they were about to sit an exam. This

There were a lot of students with quite low levels

Anxiety before exam

125 The histogram in Figure 1. 7 shows the distribution

400 600 800 1000

together into the columns. If you changed the

~EXERCISE 1.12 (Solution on page 259)

Describe the shape of each of the following distributions

~EXERCISE 1.13 (Solution on page 259)

Output from the EXPLORE procedure - Summary Statistics

Travel time Difference between travel

~EXERCISE 1.14 (Solution on page 259)

~EXERCISE 1.15 (Solution on page 259)

Output from the EXPLORE procedure - Percentiles and Boxplots

Probably the last thing that a military government might be

TRADE AND COMMERCE

Sir Rudolf von Slatin, Inspector-General of the Soudan, who

‘The colony of blacks established at Kassala continues to thrive, and in every

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