Page 130 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Unit 8: Measurement of Central Tendency

Solution: Notes

CI f Mid point (X) fX
40–44 3 42 126
35–39 5 37 185
30–34 10 32 320 Mean = “fN

25–29 14 27 378
20–24 8 22 176
15–19 6 17 102
10–14 4 12 48
N = 50 “fX = 1335
(C) Calculating the Mean through Assumed Mean Method (The short method)

In the Assumed Mean Method we try to avoid lengthy calculations of multiplications of mid-
points of class intervals with corresponding frequencies. First of all, we locate a class that lies
almost at the middle of the distribution. Its mid-point is taken as the Assumed Mean (A.M.).
Now the class intervals around this, i.e., the choosen class interval for (A.M.) would be 1,2 or
3 class intervals above and below it. So deviations from this class interval would be + 1, + 2,
+ 3 etc. and – 1, – 2, – 3 etc. in the subsequent class intervals containing higher and lower
scores respectively on the two sides. These figures are obtained by subtracting the A.M. from
the mid point of the class interval and dividing by the size of the class interval. However, this
calculation is not required in regular practice while solving the questions. This method is also
known as ‘Step Deviation Method’.
The steps involved may be summarized as below :
• Arrange the data in a tabular form i.e., making columns for class interval (CI), frequency (f),
deviation (d), and frequency x deviation (fd).
• Locate the class interval which falls midway in the distribution. If you come across two
class intervals, choose the one with greater frequency.
• Fill up the column of deviation : zero against the class interval containing A.M, and +1,
+2, +3 etc. against class intervals with larger score limits and –1, –2, –3 etc. against class
intervals with smaller score limits.

• Find out multiplications of frequency and corresponding deviation and place the obtained
value in the column headed by fd.
• Find the sum of the column fd i.e., Cfd.

• The following formula may then be applied for calculating the Mean
Mean = A.M.+ {(“f d/N)} x i

Where, A.M. = Assumed Mean
f = frequency
d = deviation from Assumed Mean
i = size of the class interval
Interpretation of Mean

Mean reprresents the centre of gravity of the scores. Measurements in any sample are perfectly
balanced about the mean. In other words the sum of deviations of scores from mean is always

LOVELY PROFESSIONAL UNIVERSITY 125