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To find mean of ungrouped data
It is obtained by adding the raw scores and dividing the sum by the number of items.
Suppose the raw scores arex1, x2, x3,…, xN
then, mean

x = each score or item
N = number of items
= sigma, which means 'summation of '
Find the mean of 6, 10, 4, 12, 8.

M = 8
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If the average weight is 56 kg, find x.

x = 58.
To find mean for grouped data
There are three methods to find mean for a frequency distribution.
(i) Direct method:
f is the frequency
M is the mean(ii) Short-cut method:
where A = assumed mean
d = x - A(iii) Step-deviation method:
where i = class size
We illustrate each of these methods with the help of the following examples.
Find the mean for the following table by the 'Direct Method'
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Direct Method:


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Short-cut Method:
(i) This method makes the calculations easy.
(ii) We assume mean as A, one of the class-marks near the middle of the 'x' column.(iii) Then, an additional column d = x - A is formed.
(iv) The mean is calculated by applying the formula.Assumed mean = A = 24.5
M = 
= 24.5 + 5.25
= 29.75![]()
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Step - Deviation Method:
Assumed mean = A = 97.5
M = 
= 97.5 - 1.6
= 95.9= 96 gm
Once you have mastered this method, statistical calculations become very easy. Large values of x are reduced to single digit numbers by Step-Deviation Method.

