Table Of ContentIntroduction to Statistics
By
Mortuza Ahmmed
Copyright © Md. Mortuza Ahmmed 2012
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Introduction to Statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data.
It deals with all aspects of this, including the planning of data collection in terms of the
design of surveys and experiments.
Applications of Statistics
Agriculture
What varieties of plant should we grow? What are the best combinations of fertilizers,
pesticides and densities of planting? How does changing these factors affect the course
of the growth process?
Business and economics
Which companies are likely to go out of business in the next year? What is the likely
tourist flow next year? What causes companies to choose a particular method of
accounting? How have living standards changed over the last six months?
Marketing Research
What makes advertisements irritating? Is an irritating ad a bad ad? Are telephone calls
the best way to collect market data? What share of the television market does Sony
have? Do higher prices signal higher quality?
Education
Does a course on classroom behavior for teachers purchased by the authority of IUBAT
have an effect on the teacher's classroom performance? Do boys perform better than
girls in the examinations? Is there evidence of sex bias in admissions to IUBAT?
Medicine
What are the important risk factors for bone cancer? What determines long term survival
after open heart surgery? Would nationwide screening for breast cancer be effective?
What projections can we make about the course of the AIDS epidemic? Is there a
relationship between drinking alcohol and breast cancer in women?
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Introduction to Statistics
Population
The entire set of individuals or objects of interest is called population.
Example
In IUBAT, there are 6000 students. All of them constitute a population.
Sample
A small but representative part of the population is called sample.
Example
In IUBAT, there are 6000 students. If we take 100 students randomly from them, these 100
students will constitute a sample.
Variable
A variable is a characteristic under study that assumes different values for different
elements.
Example
Shirt size, height of students, age, colors, sex and so on.
Qualitative Variable
Qualitative variables take on values that are names or labels.
Example
Religion, colors, sex would be examples of qualitative or categorical variable.
Quantitative Variable
A variable that can be measured numerically is called quantitative variable.
Example
Shirt size, height of students, age would be examples of quantitative variable.
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Discrete variable
A variable whose value is countable is called discrete variable.
Example
Number of mobile sets sold in a store last month, Number of patients admitted in a
hospital last month would be examples of discrete variable.
Continuous variable
A variable which can’t be counted and can assume any between two numbers is called
continuous variable.
Example
Age, weight, height would be examples of continuous variable.
Independent variable
The variable that is use to describe the factor that is assumed to cause the problem is
called independent variable.
Example
Smoking causes cancer - here smoking is the independent variable.
Dependent variable
The variable that is used to describe the problem under study is called dependent
variable.
Example
Smoking causes cancer – here cancer is the dependent variable.
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Introduction to Statistics
Scales of Measurement
Nominal scale
The variable under this measurement scale can be classified and counted but no
ordering is possible.
Example
Sex, religion, marital status
Ordinal Scale
The variable under this scale can only be classified, counted and ordering is possible.
Example
Economic status, exam grade, academic result
Interval scale
Along with all the characteristics of nominal scale and ordinal scale it includes the
different between the values which is constant.
Example
Temperature, calendar date
Ratio scale
This is the best measurement scale. It satisfies all the four properties of measurement:
identity, magnitude, equal intervals and an absolute zero.
Example
Age, height, weight, length
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Introduction to Statistics
Separate the following variables into discrete (D) and continuous(C)
Number of phone calls received in a day, Time taken to serve a customer, Weight of a
customer, Volume of a 3c.c. bottle of medicine, Size of shoes produced by BATA
D C C C D
Identify whether each of the following constitutes a population (P) or sample(S)
Kilograms of wheat collected by all farmers in a village, Credit card debt of 50 families
selected from a city, Ages of all members of a family, Number of parole violations by all
2147 parolees in a city, Amount spent on prescription drugs by 200 citizens in a city
P S P P S
Classify the following into nominal (N), ordinal (O), interval (I) and ratio(R)
Age of the pupils, Gender of the students, Health status (poor, average, well), Academic
degree (primary, secondary, higher), Hair color, Weight, Disease status (diseased, non-
diseased), Place of residence (urban-rural), Calendar time (3pm, 6pm. etc.), IQ test score.
R N O O N R N N I I
Separate the following variables into quantitative (Qn) or qualitative (Ql)
Number of persons in a family, Color of cars, marital status of people, Length of frog’s
jump, Number of students in the class
Qn Ql Ql Qn Qn
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PRESENTATION OF DATA
Frequency table
A table that shows the frequencies of each of the values of a variable under
consideration is called frequency table.
Example
Consumers were asked to rate the taste of a new diet drink as being poor (P), good (G),
excellent (E). The following data were obtained:
G P G E G G E P G G
E G E P E E G P G G
P G G E E
(i) Construct a frequency table
(ii) Add a relative frequency table to the table
Rating of Drink Tally marks Frequency Relative Frequency
P IIII 05 05 / 25 = 0.20
G IIII IIII II 12 12 / 25 = 0.48
E IIII III 08 08 / 25 = 0.32
Total 25 1.00
Bar diagram
A graph in which the classes are represented on the horizontal axis and the class
frequencies on the vertical axis is called bar diagram. Bar diagram is only used for the
qualitative variable.
Example
Students of BBA department of IUBAT are classified as follows
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Introduction to Statistics
Religion of students Frequency
Muslim 150
Hindu 100
Christians 056
Others 025
Construct a simple bar diagram
160
140
120
100
y
c
n
e
u 80
q 150
e
r Religion
F 60
100
40
56
20
25
0
Muslim Hindu Cristian Other
Religion of students
Component bar Diagram
Here bar is sub-divided into as many parts as there are components. Each part of the bar
represents component while the whole bar represents the total value.
Example
Students of the course STA 240 of summer semester are classified as follows
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Introduction to Statistics
Section A Section B Section C Section D
Male 80 60 90 70
Female 20 15 30 10
Construct a component bar diagram
140
120
30
100
s
t
n 20
e
d
u 80
st 10
of 15
er 60 Female
b
Male
m
u 90
N
40 80
70
60
20
0
Section-A Section-B Section-C Section-D
Class sections
Multiple bar Diagram
A multiple bar graph contains comparisons of two or more categories or bars.
Example
Students of the course STA 240 of summer semester are classified as follows
Section A Section B Section C Section D
Male 80 60 90 70
Female 20 15 30 10
Construct a multiple bar diagram
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100
90
80
s 70
t
n
e
d 60
u
t
s
f 50
o
r 90 Male
e
b 40 80 Female
m
70
u
N 30 60
20
30
10 20
15
10
0
Section A Section B Section C Section D
Class sections
Pie Chart:
A pie chart displays data as a percentage of the whole. Each pie section should have a
label and percentage.
Example
Students of BBA department of IUBAT are classified as follows
Religion of students Frequency
Muslim 150
Hindu 100
Christians 050
Others 025
Construct a pie chart
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