1. Presented to:
Sir Yusuf Khan
Presented by :
09040606-028
-031
-011
-001
-048
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3.  Classification
 Tabulation
 Tabulation
 Frequency Distribution
 Graphical representation
 Diagrams
 Graph

4.  Definition
“The process of dividing a set of
observation or objects into classes or Group.”
 One way classification
 Two way classification
 A manifold or cross classification

5.  TO reduce the Large sets……….
 To display points of similarity……….
 To save mental strain by eliminating………
 To reflect important aspects…………
 To prepare the ground for comparison…..

6.  Classes should be arranged so that each
observation can be placed in one and only
one class .
 Classes should be inclusive.
 The conventional classification procedure
should be adopted.
 The classification procedure should not be so
elaborate.

7. TABULATION
Systematic presentation of data classified
under suitable head and subheads and place
in columns and rows

8.  Title
 Column captions and boxhead
 Row captions and Stub
 Prefatory Notes and Footnotes
 Source Notes
 Body and arrangement of data
 Spacing and rulings

9. …….Title……
prefatory notes
Boxhea Column captions
d
units
STUB …… ……. B D …… ……
…. ... O Y …… …..
FOOT NOTES……….
SOURCE NOTES………..

10.  Frequency:
“ The number of observations
falling in a particular class is referred to as
the class frequency or simply “frequency” is
denoted by f”

11.  It is a tabular summary of a set of data that
shows that frequency or number of data
items that falls in each of several distinct
classes or simply the arrangement of data
according to magnitude is called frequency
distribution.

12.  The number or the values of the variables
which describe the classes.
 Upper class limits
 Lower class limits

13. Upper class limits
• Are the largest numbers that can
actually belong to different classes
1-3 10
4-6 14
upper
class limit 7-9 10
10-12 6
13-15 5
16-18 5

14. Lower class limits
• Are the smallest numbers that can
actually belong to different classes
1-3 10
4-6 14
Lower
class limit 7-9 10
10-12 6
13-15 5
16-18 5

15.  The class boundaries are the precise numbers
which separate one class from another, the
selection of these numbers removes the difficulty.
If any ,in knowing the class to which particular
value should be assighned e.g 0.5-3.5,3.5-
6.5,6.5-9.5
Class boundaries ( in Frequency
miles)
0.5-3.5 10
3.5-6.5 14
6.5-9.5 10
9.5-12.5 6
12.5-15.5 5
15.5-18.5 5

16. Class midpoints
• Midpoints of the classes
• Class midpoints can be found by
adding lower class limits to the upper
class limits and dividing the sum by
two.

17. Class midpoints
• Midpoints of the classes
Class limits( in miles) Frequency
123 10
456 14
Mid 789 10
points
10 11 12 6
13 14 15 5
16 17 18 5

18.  The class width of a class is equal to the
differences b/w class boundaries.
 It can also be obtain by
 Difference b/w two successive lower and
upper class limits.
 Difference b/w two successive class marks
 Denoted by h or c.

19.  Decide on the number of classes into which
the data are to be grouped.
 Determine the range variation in the data
 Divide the range variation by the number of
classes to determine the approximate width
or size of the equal class-interval

20.  Decide where to locate the class limit of the
lowest class and the lower class boundary.
 Determine the remaining class limit and class
boundaries by adding the class-interval
repeatedly.
 Distribute the data into appropriate classes.
 Total the frequency column to see that all the
datas have been accounted for.

21.  Twenty five army officers were given a blood
test to determine their blood type.the data
set is :
A B B AB O
O O B AB B
B B O A O
A O O O AB
AB A O B A

22.  It frequency distribution is:
CLASS FREQUENCY
A 5
B 7
O 9
AB 4
TOTAL 25
 Now some general observations can be obtained
from looking at the data in the form of frequency
distribution. For example, the majority officers
belonging to group O

23.  Suppose a researchers wished to do a study on the
number of miles that the employees of a large
department store travelled to work each day.The
researcher first would have to collect the data by
asking each employee the approximate distance the
store is from or his or her home.The data are:
 1 2 6 7 12 13 2 6 9 5
18 7 5 3 15 15 4 17 1 14
4 16 4 5 8 6 5 18 5 2
9 11 12 1 9 2 10 11 4 10
9 18 8 8 4 14 7 3 2 6

24. Classes Frequency
1-3 10
4-6 14
7-9 10
10-12 6
13-15 5
16-18 5
Total 50

25.  It is very hard for us to tell the information
from such a table full a raw data .Therefore
the researcher organizes the data by
constructing a frequency distribution. The
frequency is the number of values in a
specific class of distribution.

26. Graph Diagrams
simple pie diagrams Pictograms
Component
Multiple bar charts

27.  A simple bar chart consist of horizontal or
vertical bars of equal width and lengths
proportional to the value they represent.
Multiple Bar Chart
 To depict a number of related factors for
comparison various years or at a number of
places multiple bar diagrams.

28.  When the magnitude of a factor is given with
its sub factors , Each bar is further is sub
divided into components in proportion to to
the magnitude of the sub factors .
 It is also called sub-divided bars.

29.  A popular device for portraying the statistical
data by means of picture or small symbols.
Pie diagrams
 A pie diagrams is a circle that is divided into
sections according to the percentage of
frequencies in each category of the
distribution.

30. Time series historigram
cumulative f polygon
Histogram
Frequency polygon

31.  Graph present the data in a simple, clear and
effective manner.
 facilitate comparison b/w two or more than
two statistical series.
 It provide picture of a statistical series.

32.  A curve showing changes in the value of one
or more items from one period of time to the
next is known as the graph of time series .
This curve also called historigaram .

33.  A histogram consist of a set of adjacent
rectangles whose bases are marked off by
class boundaries ( not class limit) on the X-
axis and whose heights are proportional to
frequencies associated with respective
classes.

34.  A frequency polygon is a graph that displays
the data by using lines that connect points
plotted for frequencies at the midpoints of
classes.
 The frequencies represent the heights of
midpoints .

35.  When a frequency polygon or histogram is
constructed over class midpoints make it
sufficiently small for large number of
observations, is smoothed.
 And shows a continuous curve it is called
frequency curve.