These slides describe statistics topic frequency distribution. I hope students get more benefits about it.

1. FREQUENCY DISTRIBUTION
A frequency distribution is a tabular arrangement of data in
which various items are arranged into classes or groups and
the number of items falling in each class is stated. The number
of observations falling in a particular class is referred to as
class frequency or simply frequency and is denoted by "f". In
frequency distribution all the values falling in a class are
assumed to be equal to the midpoint of that class.
Data presented in the form of a frequency distribution is also
called grouped data. Data which have not been arranged in a
systematic order are called raw data or ungrouped data.
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2. CLASS LIMITS
The class limits are defined as the number or the values of the
variables which are used to separate two classes. The smaller
number is called lower class limit and larger number is called upper
class limit. For discrete variables, class boundaries are the same as
the class limits. Sometimes classes are taken as 20--25, 25--30 etc
In such a case, these class limits means " 20 but less than 25", "25
but less than 30" etc
Class Boundaries
The class boundaries are the precise numbers which separate one
class from another. The main object to defined class boundaries is
to removes the difficulty, if any, in knowing the class to which a
particular value should be assigned. The class boundary is located
midway between the upper limit of a class and the lower limit of
the next higher class.
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3. CLASS MARKS OR MIDPOINTS
The class mark or the midpoint is that value which divides a
class into two equal parts. It is obtained by dividing the sum
of lower and upper class limits or class boundaries of a class
by 2.
CLASS INTERVAL
Class interval is the length of a class. It is obtained by
I. The difference between the upper class boundary and the
lower class boundary. (Not the difference between class
limits).
II. The difference between either two successive lower class
limits or two successive upper class limits.
III. The difference between two successive midpoints.
Auniform class interval is usually denoted by "h".
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4. CONSTRUCTION OFAFREQUENCY DISTRIBUTION
Decide the number of classes
No hard and fast rule for deciding on the no of classes.
Statistical experience tells us that no less than 5 and no more
than 20 classes are generally used.
The number of classes is determine by the formula i.e K=1+3.3
log(n). Where K denotes the number of classes and n denotes
the total number of observations.
Determine the range of variation of the data.
The difference between the largest and smallest values in the
data is called the range of the data. i.e
R = largest observation - smallest observation
Where R denote the range of the data.
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5. Determine the approximate size of class interval
The size of the class interval is determine by dividing the range
of the data by the number of classes i.e h= R/K
Where h denotes the size of the class interval. In case of
fractional results the next higher whole number is usually taken
as the size of the class interval.
Decide where to locate the class limits
The lower class limit of the first class is started just below the
smallest value in the data and then add class interval to get
lower class limit of the next class, repeat this process until the
lower class limit of the last class is achieved.
Distribute the data into appropriate classes
Take an observation and marked a vertical bar "I"(Tally) against
the class it belongs.
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6. Example
The following data is the final plant height (cm) of thirty
plants of wheat. Construct a frequency distribution
87 91 89 88 89 91 87
92 90 98 95 97 96 100
101 96 98 99 98 100 102
99 101 105 103 107 105 106
107 112
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7. Step- 1: Calculate the Range
R = Largest observation - Smallest observation
= 112 - 87 = 25
Step- 2: Number of classes
The number of classes is determine by the formula
K = 1+3.3 log (n) = 1+3.3 log(30)= 1+3.3(1.4771)= 5.87 = 6
Step-3: Size of class interval
The size of the class interval h= R/K
h = 25/6 = 4.17 = 5
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8. Step- 4: Choose the lowest value
Minimum Value = 87, so start the class interval from 86.
Step-5: Calculate the mid point
Average of lower and upper class limits
Step- 6: Convert the class limits to class boundaries
h
2
m idpiont 
Step-7:Assigned the observations to the Classes
Starting from first observation and assigned the
observation to the classes they belong. Tally mark is
made in the tally column against this class.
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9. The following data is the final plant height (cm) of thirty
plants of wheat.
87 91 89 88 89 91 87
92 90 98 95 97 96 100
101 96 98 99 98 100 102
99 101 105 103 107 105 106
107 112
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10. Class
Limits
Class Mi -
Points
Entries Tally
IIII I
IIII
f c.f.
6
Boundaries
8 ---- 90 85. --- 90.5 88 87,89,88,89,87,90 6
4
9 ---- 95 90. --- 95.5
9 -- 100 95. -- 100.5
93
98
91,91,92,95 10
98,97,96,100,96,98,99,98,
100,99
IIII IIII 10 20
10 105
10 110 105 110.5
11 115 110 115.5
100 105.5 103
108
113
101,102,101,105,103,105 IIII I
III
6
3
26
29
30
107,106,107
112 I 1
Total 30
Frequency distribution of the height of plants.
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11. FREQUENCY DISTRIBUTION TABLE
Class Class Mid Tally Freq C.F
uency
Limits Boundaries Points
(f)
8 - 90 85. - 90.5 88 /////
9 - 95 90. - 95.5 93 ////
6 6
4 10
9 - 100 95. - 100.5 98 //////// 10 20
10 - 105 100. 105.5 103 /////
10 - 110 105. – 110.5 108 ///
11 - 115 110. 115.5 113 /
6 26
3 29
1 30
30
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12. Example
Suppose we walk in the nursery class of a
schoo and we coun the n o Books and copies
tha 4 student have in thei bag .
Suppos th n o book and copie are
,
, ,
, .

13. Representation of Data in a Discrete
Frequency Distribution
X
3
4
Tally
|
Frequency
1
3
|||
5
6
7
8
|||| ||||
|||| |||| |||
|||| ||
|||
9
13
10
3
9 |||| | 6
Total 45

14. Relative Frequency Distribution
X Frequency Relative/ %age
Frequency
3 1 1/45 x 100 = 2.22%
4 3
9
3/45 x 100 = 6.67%
9/45 x 100 = 20%
5
6 13
10
3
13/45 x 100 = 28.89%
10/45 x 100 = 22.22%
3/45 x 100 = 6.67%
6/45 x 100 = 13.33%
7
8
9 6
Total 45

15. Cumulative Frequency Distribution
X Frequency Cumulative
Frequency
1
3 1
3
4 1+3 = 4
4+9 = 13
5 9
6 13
10
3
13+13 = 26
26+10 = 36
36+3 = 39
39+6 = 45
7
8
9 6
Total 45

16. ◼ Frequency
The number of values falling in a particular category
◼ Cumulative frequency
Sum of the observed frequency plus all above class frequencies
◼ Notations
X,Y,Z, n, N ∑ (Summation)
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