STATISTICS (2 ND SEM) Statistics often involves three kinds of

data; namely, metric, enumeration and

LESSON 1: INTRODUCTION TO categorical data.
STATISTICS
STATISTICS - a branch of mathematics
that deals with the collection, 1. Metric data – Obtained by
organization, presentation, analysis, and measurement.
interpretation of data.
Examples:
STATISTIC - refers to a numerical data - Height of first year students in
or an estimate of some quantities, such as your school.
an average or measure of scatter. It is - Age of fathers in your
referred also to numerical datum gathered neighborhood.
from the surveys and census as score or - Scores in the entrance exam of
observation. the incoming freshmen students.
HOW STATISTICS WORK?
Statistics starts with a question, not with 2. Enumeration data – Obtained by
the data or information. counting.
Every time, we use statistics to find the
solution for a question. Examples:
- How many professionals in your
Statistics are what the decision-makers barangays are single and married?
can use to reduce inappropriate outcome - How many parents are working
by qualifying it. abroad?
- How many students have
All statistics are based on data.
separated parents?
Data are what we hear, see, smell, touch
and etc.
3. Categorical date – Can be
Data requires measuring.
classified intro groups or
Good measurement gives good data categories of responses
Good data give better answer than bad Example:
data - Attitudes of workers in a
But all data will give you all the answers. company towards their superiors.
- Personality traits of teachers in
CENSUS is an official, usually periodic, your school
counting of population. It is a collection - Level of stress suffered by takers
of data from every element in a of entrance examination.
population.
POPULATION is a complete collection
Examples: of all elements (scores, people,…) to be
1. How much our population has grown? studied.

2. How many are employed, unemployed, SAMPLE is a sub collection of elements

and underemployed drawn from a population.
TYPES OF SAMPLES: Ex:
1. Number of students enrolled in
1. Random sample – Each member
a semester.
of the population has an equally
2. Number of vehicular accidents
likely chance of being selected.
in Cainta.
2. Convenience sample – A sample
Continuous Data – Result from
that is chosen so that it is easy for
infinitely many possible values
the researcher.
that can associate with points on a
continuous scale in such a way
3. Stratified random sample – The
that there are no gaps or
population is divided into
interruptions. It is one whose
subgroups, so that each
values are real numbers.
population member is in only one
subgroup.
Ex:
1. Daily wind speed.
Example: Group of people by age
2. Weight of newborn babies.
and how much they earn in a
3. Temperature of a freezer.
year.

4. Cluster sample – Sample that

Another way to classify data is to use four
consists of items in a group such
levels of measurements: Nominal, ordinal,
as a neighborhood or a household.
interval, and ratio.
Used in a big population.
1. Nominal Level of measurement
5. Systematic sample – Obtained – Characterized by data that
using an ordered list of the consist of names, labels, or
population, selecting members categories only. The order does
systematically from the list. not matter.

Ex. Jersey numbers in basketball

THE NATURE OF DATA
2. Ordinal level of measurement –
Quantitative data – Numbers
Involves data that may be
representing counts or measurements.
arranged in some order but
Qualitative data – Can be separated into differences between data values
different categories that are distinguished either cannot be determined or are
by some non-numeric characteristics. It meaningless. The order matters.
can be either discrete or continuous.
Ex. Place finished in a race – 1st,
Discrete data – Result from 2nd, 3rd, and so on.
either a finite number of possible
values or countable number of 3. Interval level of measurement –
possible values. It is one which Like the ordinal level, the order
can take integral values or whole matters, but it is meaningful
numbers. amounts of differences between
data can be determined (except
 ratios). It has no inherent (natural) 2. Questionnaire – An inventory of
zero staring point. None of the information listed down to which
quantity is present. a respondent answer.

Ex: Temperature 3. Registration or Census –

Requires the enactment of law to
4. Ratio level of measurement – take effect for it needs the
The interval level modified to participation of a large, if not the
include the inherent zero starting entire, population.
point.
4. Observation – It makes use of
Ex. Weight in pounds or grades the different human senses in
in test. gathering information.

5. Experimentation – Conducted in
laboratories where specimens are
subjected to some aspects of
control to find out cause and
effect relationship.

METHODS OF PRESENTING DATA

1. Textual method – Presents the
collected data in narrative and
paragraph form.

AREAS WE USE STATISTICS 2. Tabular method – Presents the

collected data in table which
1. Business and Industry orderly arranged in rows and
columns for an easier and
2. Health and Medicine comprehensive comparison of
figures.
3. Learning
3. Graphical method – Presents the
4. Research collected date in visual or
pictorial form to get clear view of
5. Social Statistics data.

6. Natural Resources

METHODS OF COLLECTING DATA

1. Interview – Refers to direct
method of gathering data since
this requires a face-to-face
inquiry with the respondent.
LESSON 2 – ORGANIZATION AND KINDS OF GRAPHS
PRESENTATION OF DATA AND
1. Line graph – Represent
FREQUENCY DISTRIBUTION
changes in data over a period
of time. Represented by
points and are joined by line
Methods of Data Presentation
segments.
A. Textual form of presentation –
Make use of words, sentences and 2. Bar Graph – Comparisons of
paragraph in presenting data numerical values of a given
collected. item over a period time. May
be made by the use of bars.
B. Tabular form of presentation –
Classifying related numerical The vertical bars consist of
facts in horizontal arrays called equal spaced vertical
lines or rows, and vertical arrays rectangles placed on a
called columns. common horizontal; base line.

The space common to a particular The heights of rectangles are

row and column is called a cell. proportional to the magnitude
represented.
A table consists of the following
parts:
3. Pie Graph - is used to form
Table of heading – Centered percentage chart or when
above the table. It consist of the wants to represent the
title of the table and the table composition by parts of a
number usually written in Hindu whole. This is a circle whose
Arabic or Roman numeral. area is divided into
component parts of sector.
Stub – Given at the left.
Describes the data found in rows
of the table. They give the 4. Pictogram or Pictograph -
classification or categories. make used of pictures and
symbols to immediately
Caption or box heading – This suggest the nature of the data
gives the designation of the being shown.
column.

Body – Constitutes the main part FREQUENCY DISTRIBUTION

of the table and contains figures TABLE - refers to the tabular
to be presented. arrangement of data by classes or
categories together with their
corresponding class frequencies.
C. Graphical Presentation – Using
graphs, symbols or visual aid.
CONTENTS OF A FREQUENCY  GREATER THAN
DISTRIBUTION TABLE CUMULATIVE FREQUENCY
– when the cumulative frequency
CLASS INTERVAL – group the data
of the lower limit is greater than
into the desired class size or desired
the cumulative frequency of the
number of cases. The class interval
class interval in the higher limit.
condensed the data so that better
observation and interpretation of data can
be made, but in so doing we lose the
identity of the individual observations of
data in the sample. A class interval is
defined by a lower limit and the higher
limit.
CLASS FREQUENCY - refers to the
number of observations belonging to a
class interval or the number of times a
class interval or items within a category.
CLASS BOUNDARY - gives the true
limit between two class intervals. It is
defined by higher limit and lower limit.
The higher limit is obtained by adding 0.5
to the upper limit of the class interval.
The lower limit is obtained by subtracting
0.5 from the lower limit of the class
interval.
CLASS MARK - is half the distance
between two class intervals. This is
obtained by adding the two class interval
divided by two.
FREQUENCY POLYGON - is a line
graph of the frequency distribution.
CUMULATIVE FREQUENCY is the
sum total of the successive frequencies
from the lowest class interval or the
highest class interval.
< LESS THAN CUMULATIVE
FREQUENCY - when the cumulative
frequency of the classes in the lower limit
is less than the cumulative frequency of
the scores in the higher limits.