MU123 Week 4 Unit 4 11

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‫‪Week 4‬‬
‫‪MU123 - Discovering Mathematics‬‬
‫‪Book A - Unit 4 + Unit 11 Book D‬‬
‫‪1‬‬
‫ ﻻﺳﺘﻼﻡ ﺍﺧﺒﺎﺭ ﺍﻟﺠﺎﻣﻌﺔ ﻭﺍﻻﻧﻀﻤﺎﻡ ﻟﻘﺮﻭﺑﺎﺕ ﺍﻟﻤﻮﺍﺩ ﻭﺍﻻﺟﺎﺑﺔ ﻋﻠﻰ ﺍﺳﺘﻔﺴﺎﺭﺍﺗﻜﻢ‬94981522
The material of this week will cover Unit 4 - Book

A (Statistical Summaries) and Unit 11 from Book
D ( Statistical Pictures). This would help you in
preparing your TMA.
2
MU123 - Discovering Mathematics AOU – ITC – Kuwait Branch
Unit 4: Statistical Summaries

This unit includes the following sections:
• Questions
• Dealing with data
• Summarising data: Location
• Summarising data: Spread
• Measuring with accuracy and precision

• Statistical Pictures (Unit 11)
• Discussing TMA
3
What is Statistics?
It is the study of the collection, organization, analysis, interpretation,
and presentation of data.
See below application areas of statistics
• Economics • Engineering
• Forecasting • Construction
• Demographics • Materials
• Sports • Business
• Individual & Team • Consumer Preferences
Performance • Financial Trends
4
Statistical thinking and Question:

e.g. Should people stop smoking???? YES but we need
statistical evidence
This unit deals with statistical thinking. It starts with
questions that can be addressed by statistical methods.
Statistical information is all around you and arises as an
attempt to answer questions of various kinds. (e.g.
Should people stop smoking?)
Statistical thinking is presented as a helpful way of
seeing the world quantitatively. For examples: table of
numbers, graphs & charts.
5
Types of statistical investigation

• Summarizing : reducing information.
– How old are students studying MU123?
• Comparing : Difference between two things.

– Are students studying MU123 older or younger
than students in IT courses?
• Seeking a relationship: relationship between quite
separate things.
– Are the numbers of road deaths in different
countries linked to their respective maximum
speed limits?
6
Types of statistical questions: Examples
• Summarizing questions:
Summarizing information is by reducing the many figures
to just one representative number or using charts or
plots. Examples of investigations:
- How many people die from road accidents each day.
- How old are the students studying MU123.
• Comparing questions:
Comparing investigation is to decide whether or not
there is a difference between two things or comparing
between two averages. Examples are:
- Do more people, on average, die from road accidents
on weekdays or at weekends?
- Are students studying MU123 older or younger than
students studying LB160?
7
Types of statistical questions: Examples.
• Relationship Questions:
Investigations could be a relationship between quite
separate things. What the relationship is. For example:
- As the numbers of road deaths in different countries
linked to their respective speed limits?
- What is the connection between the numbers of
hours that students work on a level 3 course in
mathematics and their final grade.
Discuss in the class Activities I and 2 (page 179) and
distinguish between the three types of statistical
investigations.
8
The statistical investigation cycle

There are four stages in most statistical investigations:
PCAI
P: Posing a question. This is the start of the investigations.

C: Collecting data, choosing samples or design a survey.
A: Analyze the data, calculating averages and plotting graphs
I: Interpreting the results, takes the action back and see whether
the data analysis help to answer the posed question.
(Check Activities 3 and 4 for complete example)
9
‫‪Activity‬‬
‫‪10‬‬
‫‪MU123 - Discovering Mathematics‬‬ ‫‪AOU – ITC – Kuwait Branch‬‬
Dealing with Data
• Primary Data: are those that you have collected yourself. The
popular ways to collect primary data consist of surveys,
interviews and focus groups.
• Secondary data: originate elsewhere. They already exists and can
be used for your purpose.
• Dataset: Is a collection of data in tabular form.
Take a quick look at the dataset at page 184. Explain the
rows and columns. Solve Activity 6.
Discrete data are data that can take one of a particular set of
values. e.g. Number of days in a week you study, or number of
websites you visit per day.
Binary data: are the data coded by two numerical values: 0 , 1.
Solve activity 9
11
‫‪12‬‬
‫‪13‬‬
Checking and Cleaning Data
• Large datasets may contain plenty of missing data.
14
Summarizing data: Location

• Stage A of the PCAI cycle
• Analyzing the data that have been collected.
• Location of a dataset is a single number that
represents an average, typical or central value.
Measuring Location:
• The three most common measures of location are:
 Mean
 Mode
 Median
15
Mean of a dataset
Definition Example
Mean: The sum of a set of
numbers, divided by how 2, 3, 3, 5, 8, 12
many numbers were
2  3  3  5  8  12
summed mean 
6
 5.5
16
Mean of a dataset
Find the mean for the sample measurements

3, 5, 1, 8, 6, 5, 4 and 6.
3  5 1 8  6  5  4  6
The mean is
8
38
  4.75
8
17
‫‪Median of a dataset‬‬
‫‪18‬‬
If there is an odd number of data values
19
If there is an even number of data values
20
‫‪Mode of a dataset‬‬
‫‪21‬‬
Mode of a dataset
• If no measurements occurring more than once, then
there is no mode.
• There may be several modes if there are more than
one data with the same most frequently occurring.
• e.g. 2, 4, 5, 1, 7, 9, 0 : No mode
2, 4, 2, 5, 4, 2 : Mode is 2
2, 4, 2, 5, 4, 2, 4, 7 : Modes are 2 and 4
22
4. Summarizing data: Spread
• Property of data which tells you how widely the

values are spread from each other.
• The most common measures of spread are:
 Range
 Interquartile range Standard deviation (IQR)
23
Range
• Range = Max  Min
24
Interquartile Range IQR
25
Interquartile Range IQR = Q3 - Q1
26
Standard Deviation
Standard deviation (SD) is the best known measure of
spread.
To find the SD, follow the following steps:
• Find the mean of the dataset
• Find the difference of each value from the mean – these
are deviations, ‘d’
• Square each deviation – ‘d²’
• Find the mean of this squared deviations – this number is
the ‘mean squared deviation’ – variance.
• Find the square root of the variance to get the standard
deviation.
27
Standard Deviation: Example

Assume that we have the following data: 1, 2, 4, 6, 7
Solve Activity 26
28
Unit 11. Statistical pictures Section 2: Histograms, bar
charts, pie charts
2.1 Histogram (Continuous data)
Exercise:
Consider the dataset below, which consists of the weights in
kilograms of 32 women at the start of their pregnancies.
54.5 9.1 73.2 41.4 55.5 70.5 76.4 70 52.3 83.2 64.5 49.5 70
52.3 68.2 47.3 66.8 70 56.4 53.6 59.1 44.5 55.9 57.3 69.5
73.2 62.7 73.6 70 56.7 58.2 68.2
A class is one of the

categories.
The class frequency is the
number of observations in a
particular class.
29
Section 2: Histograms, bar charts, pie charts
2.2 Bar charts (Discrete data)
Exercise:
The bar chart below shows the frequencies with which the six
scores 1, 2, 3, 4, 5, 6 cropped up as a result of 30 rolls of a die.
30

2.2 Bar charts (Categorical data)
Exercise:
Major Count 150
Accounting 130
100
Economics 20
Management 50 50
Total 200 0
Acct. Econ. Mgmt.
Major
31
2.4 Pie Charts (Categorical data)
1. Shows breakdown of total quantity into categories
2. Useful for showing relative differences Mgmt.
25%
3. Angle size = (360°)(percent)
Econ.
10% 36°
Major % Angle
Accounting 65 234 Acct.
Economics 10 36
65%
Management 25 90
Total 100 360

Revision:
The four stages of a statistical investigation cycle PCAI

Stage 1 Pose a question
Stage 2 Collect relevant data
Stage 3 Analyze the data
Stage 4 Interpret the results
33
Revision:
Recall Activity:
Here are nine of the common types of task that tend to arise in
the C, A and I stages of a statistical investigation. Try to match
each task to one of these three stages
1. Calculate an average
2. Calculate a percentage
3. Choose a set of values, or sample
4. Make a decision based on an observed, numerical difference
5. Design a questionnaire
6. Draw a conclusion
7. Draw a helpful graph
8. Key the data into a spreadsheet
9. Make a prediction about the real world
34
…..Discussing the TMA
Important:
Please solve all activities and Compare your
answer with answers
Provided on your book.
35

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‫‪ 94981522‬ﻻﺳﺘﻼﻡ ﺍﺧﺒﺎﺭ ﺍﻟﺠﺎﻣﻌﺔ ﻭﺍﻻﻧﻀﻤﺎﻡ ﻟﻘﺮﻭﺑﺎﺕ ﺍﻟﻤﻮﺍﺩ ﻭﺍﻻﺟﺎﺑﺔ ﻋﻠﻰ ﺍﺳﺘﻔﺴﺎﺭﺍﺗﻜﻢ‬

‫‪MU123 - Discovering Mathematics‬‬

‫‪Book A - Unit 4 + Unit 11 Book D‬‬

The material of this week will cover Unit 4 - Book

Unit 4: Statistical Summaries

• Measuring with accuracy and precision

Statistical thinking and Question:

Types of statistical investigation

• Comparing : Difference between two things.

The statistical investigation cycle

P: Posing a question. This is the start of the investigations.

Checking and Cleaning Data

• Large datasets may contain plenty of missing data.

Summarizing data: Location

Find the mean for the sample measurements

• Property of data which tells you how widely the

Standard Deviation: Example

A class is one of the

Section 2: Histograms, bar charts, pie charts

Total 100 360

The four stages of a statistical investigation cycle PCAI

…..Discussing the TMA

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