This presentation is containing basic of Statistics, like meaning of statistics, definition, different types of data and its representation methods.

1. 1
Introduction to Statistical Methods
By Tushar Bhatt, Assistant Professor in Mathematics, Atmiya University, Rajkot. 5/25/2020
By
Tushar J Bhatt
[M.Sc (math's),M.Phil (Math's),M.Phil (stat.),M.A(Education), P.G.D.C.A, Ph.D (math's)-pursuing)
Assistant Professor in Mathematics
Atmiya University-Rajkot
Gujarat(India)

2. 2
Module
1 Statistics – Definition and Scope
OUTLINE ( Teaching Hours - 5)
1. Introduction
2. Sample and Population
3. Data Analysis : Classifications and Tabulations
4. Graphical representation and its interpretations
By Tushar Bhatt, Assistant Professor in Mathematics, Atmiya University, Rajkot. 5/25/2020

3. 3
Meaning of word Statistics
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Latin word Italian word German Word
Equal Meaning
Political State

4. 4
Meaning of word Statistics
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot. 5/25/2020
Ical
(Management)
Geographical
management
Demographical
Management
Economical
Management
Containing : Boundary
management, Culture of
region etc
Containing:
Emotions of
People, Locality
etc.
Containing:
Income, Departu
re and etc.
There is associate
with 3-types of
managements

5. 5
Meaning of word Statistics
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Therefore the word statistics is associate with, the study of economy,
demography and geography of any state or country.
 The statistics is a science which deals with presentation, interpretation,
collection and analysis of data.
Definition : Data
The data is collection of facts or relevant information‘s.
Definition : Row data
The row data is the data , in original form before any statistical computation
used.

6. 6
Types of data
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0
Row data
Primary
Data
Is a data which are
collected by a person or an
organization for its own
use only
Secondary
Data
Is a data which are
collected by another
person or an organization
for its own use only but
investigator is also used it.

7. 7
Classification of data
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
The classification of data is scientific process in which the data divided
into certain categories according to resemblances.
Classification
on the basis
of Social
Status
Qualitative
Data
on the basis
of Numerical
Size
Quantitative
Data
on the basis
of Time
Temporal
on the basis
of Location
and Place
Geographical

8. 8
Classification of Data
 Qualitative
When the basis of classification according to characteristics like social
status and etc., is called qualitative data.
 For example : 1. Reach and Poor Persons
2. Educated and Uneducated Persons etc.,
 Quantitative
When the basis of classification according to differences in quantity means
is made according to a numerical size is called quantitative data.
 For example : 1. A class of students split up into groups according to their
heights or ages.
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020

9. 9
Classification of Data
 Temporal
The classification according to time is called temporal classification of data
 For example : 1. The students who got first class during the last three
years are classified year wise.
 Geographical
The classification according to geographical location or place is called
geographical classification of data.
 For example : 1. The production of wheat (in quintals) in different states.
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
 According to above classification of data, the quantity which is vary from
one to another is called a variable.

10. 10
Types of Variable
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Individual
Discrete
Continuous
Variable
Data which are separate
by comma’s and like a
sequence of numbers
Data with
frequency
Data distributed
in classes with
frequency

11. 11
Tabulation of Data
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
The last stage in compilation of data is tabulation.
 After the data have been collected and classified , it is essential to put
them in the form of tables with rows and columns.
Tabulation is a scientific process used in setting out the collected data
in an understandable form.

12. Ex-1 : In 1990, out of a total of 2000 students in a college 1400
were from graduation and the rest for post – graduation. Out
of 1400 graduates students 100 were girls. However in all
there were 600 girls in the college. In 1995, number of
graduates students increased to 1700 out of which 250 were
girls, but the number of post – graduate fall to 500 of which
only 50 were boys . In 2000, out of 800 girls 650 were from
graduation , whereas the total number of graduates was 2200.
The number of boys and girls in post – graduation classes was
equal. Represent the above information in tabular form. Also
calculate the percentage increase in the number of graduate
students in 2000 as compared to 1990.
Tabulation
12By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0

13. Tabulation
13By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Year UG PG Total
(a)+(b)
B G T(a) B G T(b)
1990 1300 100 1400 100 500 600 2000
1995 1450 250 1700 50 450 500 2200
2000 1550 650 2200 150 150 300 2500
Total 4300 1000 5300 300 1100 1400 6700
Increment the number of students in % as
1400------------100 | % = (800/1400)*100 = 57.14
800 ------------ ? |

14. Ex-2 : In a sample study about coffee habit in two towns in the
year 1990, the following information was received :
• Town A : Females were 40% , total coffee drinkers were 45%
and males non – coffee drinkers were 20%.
• Town B : Males were 55% , Males non- coffee drinkers were
30% and female coffee drinkers were 15%.
Present the above data in a tabular form.
Tabulation
14By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020

15. Tabulation
15By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Town A
Town B
M F Total M F Total
Coffee drinkers 40 5 45 25 15 40
Non-Coffee
drinkers 20 35 55 30 30 60
Total 60 40 100 55 45 100
Solution -2

16.  There are 3 – methods to represent the Ungrouped data in
graphical way :
a) Pictograms
b) Bar Charts
c) Pie Diagrams
Graphical Representations of Discrete data
16By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
a) Pictograms :
 In this representation method the ungrouped data in
which represent the frequency by horizontal line and
square.

17. Graphical Representations of Discrete data
17
Ex – 3 : The number of television sets repaired in a workshop
by a technician is six, one month period is as shown below.
Present these data as a pictogram.
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0
Month Jan. Feb. Mar. Apr. May Jun.
No. of TV Repaired 11 06 15 09 13 08
Solution -3
Here given data set on pictogram first we have to set the
symbol for representation of data, so we are assume that a
square = 2 unit

18. Graphical Representations of Discrete data
18By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Month No. Of TV set repaired = 2
January
February
March
April
May
June

19. b) Bar Charts :
 Bar Charts is a representation of a numbers using bars of
uniform width and length of bars depends upon frequency
and scale you have chosen.
Graphical Representations of Discrete data
19
Horizontal
Bar charts
Vertical
Bar charts
 The data represent by equally
spaced in horizontal rectangles
 Rectangles parallel to X -axis
The data represent by equally
spaced in vertical rectangles
 Rectangles parallel to Y – axis
By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020

20. Ex-4 : The distance in kilometers travelled by 4- salesman in a
week are as shown below :
Use a horizontal bar chart to represent these data
diagrammatically.
Graphical Representations of Discrete data
20By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0
Salesman
(Y)
P Q R S
Distance
Travelled
(X)
413 264 597 143

21. Graphical Representations of Discrete data
21By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
0 200 400 600 800
P
Q
R
S
Distance Travelled in Km by a salesman
Distance Travelled in Km
by a sales man
Solution -4

22. Ex-5 : The number of tools from a store in a factory is
observed for seven , one –hour period in a day and the
results of the survey are as follows :
Present these data on a vertical bar chart.
Graphical Representations of Discrete data
22By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0
Period(X) 1 2 3 4 5 6 7
No. Of issues (Y) 34 17 9 5 27 13 6

23. Graphical Representations of Discrete data
23By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7
No of tools issues by factory in one -hour period
No of tools issues by
factory in one -hour
period
Solution -5

24. (C) Pie Chart :
 The pie chart is represented by a circle.
 The are of circle represent the whole and the area of
sectors of the circle are proportional to the part which
make up the whole.
Graphical Representations of Discrete data
24By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
* Steps for making a Pie Chart :
Step -1 : Find total
Step – 2 : Convert into %
Step -3 : % convert into degree
Step – 4 : Arrange in ascending order
Step – 5 : Plot and Label.

25. Ex-6 : In IGNOU university year 2005 , course wise admission
data is given below :
Represent the above data on pie chart.
Graphical Representations of Discrete data
25By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0
Course Number of
students
M.A 200
M.com 600
M.Sc 400
M.B.A 800

26. Graphical Representations of Discrete data
26By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Solution -6
Courses
No. Of
students
% Deg.
Increasing
order
M.A 200 10% 36 1
M.com 600 30% 108 3
M.Sc 400 20% 72 2
M.B.A 800 40% 144 4
TOTAL 2000 100% 360 ----------

27. Graphical Representations of Discrete data
27By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
M.A
10%
M.Sc
20%
M.Com
30%
M.B.A
40%
No. Of students in various courses of IGNOU
university in year 2005
Solution -6
Total number of students =2000

28. Graphical Representations of Continuous data
28By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
o The Graphical representation of grouped data is classified into
3-categarioes :
(a) Histogram
(b) Frequency Polygon
(c) Ogive

29. Graphical Representations of Continuous data
29By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
(a) Histogram :
 The histogram is mainly used for presentation of grouped data in
which the respective frequency of the classes are plot on a graph as
a vertical adjacent rectangles.
 If class intervals are of equal length then the heights of rectangles
of a histograms are equal to frequencies.
 If lower bound of the first class is not same as upper bound of the
next class then using the following procedure make them equal
1. Upper class boundary+0.5
2. Lower class boundary -0.5
 If class intervals are of not equal length then the heights of
rectangles of a histograms are obtain by using following manner:
1. Find Class Length(CL)
2. New frequency = (f/CL)* Lowest CL

30. Graphical Representations of Continuous data
30By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020

31. Graphical Representations of Continuous data
31By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020

32. Graphical Representations of Continuous data
32By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Ex- 7 : Construct a histogram from the following tabular data :
Class Frequency
70-72 1
73-75 2
76-78 7
79-81 12
82-84 9
85-87 6
88-90 3

33. Graphical Representations of Continuous data
33By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Solution- 7 :
Here upper bound of the first class and lower bound of the second
class not equal therefore, make them equal first.
Class Equal Class Frequency
70-72 69.5-72.5 1
73-75 72.5-75.5 2
76-78 75.5-78.5 7
79-81 78.5-81.5 12
82-84 81.5-84.5 9
85-87 84.5-87.5 6
88-90 87.5-90.5 3

34. Graphical Representations of Continuous data
34By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020

35. Graphical Representations of Continuous data
35By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Ex- 8 : Construct a histogram from the following tabular data :
Class Frequency
1-2 5
2-3 3
3-5 6
5-7 12
7-10 9
10-15 10
15-17 4

36. Graphical Representations of Continuous data
36By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Solution : 8
Class Frequency (f)
Class Length (CL)
(f/CL)*Lowest CL = New
Frequency
1-2 5 1 (5/1)*1 =5
2-3 3 1 (3/1)*1 = 3
3-5 6 2 (6/2)*1=3
5-7 12 2 (12/2)*1=6
7-10 9 3 (9/3)*1=3
10-15 10 5 (10/5)*1 =2
15-17 4 2 (4/2)*1 =2

37. Graphical Representations of Continuous data
37By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Solution : 8

38. 38By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0
Graphical Representations of Continuous data
(b) Frequency Polygon :
 The Frequency Polygon is a graph obtained by plotting
frequency against mid-point values and joining the
coordinates with straight lines.
 If the class intervals are very small then the frequency
polygon assumes the form of a smooth curve known as the
frequency curve.

39. 39By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/202
0
Graphical Representations of Continuous data
Ex-9 : Draw the frequency polygon for the data given in
following table :
Class Mid-Point Frequency
7.1-7.3 7.2 3
7.4-7.6 7.5 5
7.7-7.9 7.8 9
8.0-8.2 8.1 14
8.3-8.5 8.4 11
8.6-8.8 8.7 6
8.9-9.1 9.0 2

40. 40By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Graphical Representations of Continuous data
Solution : 9
0
2
4
6
8
10
12
14
16
7.2 7.5 7.8 8.1 8.4 8.7 9
Frequency
Frequency Polygon
Class Mid-Point

41. 41By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Graphical Representations of Continuous data
(C) Ogive or Cumulative Frequency Distribution curve :
 The curve is obtained by joining the coordinates of
cumulative frequency (vertically ) against upper class
boundary ( horizontally) is called an Ogive or Cumulative
Frequency Distribution curve .

42. 42By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Graphical Representations of Continuous data
Ex-10 : The frequency distribution for marks of 50 students is given
in the following table. Form cumulative frequency
distribution for these data and draw the corresponding Ogive.
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
2 4 10 4 3 8 1 5 11 2

43. 43By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Graphical Representations of Continuous data
Solution : 10
Class Frequency Upper class
Boundary
Cumulative
frequency
0-10 2 10 2
10-20 4 20 6
20-30 10 30 16
30-40 4 40 20
40-50 3 50 23
50-60 8 60 31
60-70 1 70 32
70-80 5 80 37
80-90 11 90 48
90-100 2 100 50

44. 44By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Graphical Representations of Continuous data
0
10
20
30
40
50
60
10 20 30 40 50 60 70 80 90 100
CumulativeFrequency
Ogive
Ogive
Upper class boundary value in marks

45. 45By Tushar Bhatt, Assistant Professor in
Mathematics, Atmiya University, Rajkot.
5/25/2020
Thank You