Page 129 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Methodology of Research and Statistical Techniques

Notes Calculating Mean for Grouped Data

There can be two situations of grouped data :
(i) when scores and frequencies are given; and
(ii) when data have been grouped i.e., frequency is given for each class interval. In the
second case we may compute either by long method or by the short method, using the
Assumed Mean. These are explained below :
(A) Calculating Mean when Scores and Frequencies are given

Example

Compute Mean for the following data :
Score 18 20 24 35 42 48 50
Frequency 2 4 3 8 6 4 3
Solution : We use the following formula :
Mean = “f x/N
Where, X = Score, f = frequency
N = “f = total number of cases (frequencies)

Scope
X f fX
18 2 36
20 4 80 Mean = “fX/N
24 3 72 = 1062/30
35 8 280 = 35.4

42 6 252
48 4 192
50 3 150
N = 30 “fX = 1062
(B) Calculating Mean from Grouped Frequency Distribution
When grouped frequency distribution is given, the Mean is calculated using the above formula
i.e.,
Mean = “fN/N
Where, X = Mid point of the class interval
f = Frequency
N = “f Total number of cases

Here an assumption is made that all frequencies are concentrated at the mid point of the class
interval. So mid points of class intervals are used for scores.

Example
Compute the mean for the following frequency distribution :

Class Interval 10-14 15-19 20-24 25-29 30-34 35-39 40-44
Frequency 4 6 8 14 10 5 3

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