Short Cut Method for Finding Mean of Grouped Data (Not in Classes) –
Under this method, larger quantities get converted into smaller ones, making the process of multiplication and division easier.
Method – From the given data, we suitably choose a term, usually the middle term and call it the assumed mean, to be denoted by A. We find the deviations, dₐ = (xₐ - A) for each term.
∑fₐdₐ
Then we should apply the formula => Mean = (A + --------)
∑fₐ
Example.1) Using short cut method, find the mean from the following data.
Variate (xₐ) 18 19 20 21 22 23 24
Frequency (fₐ) 184 212 327 376 614 372 415
Ans.) Let, the assumed mean be, A = 21
From the given data, we prepared the table given below –
Variate (xₐ) Frequency (fₐ) dₐ = (xₐ - A) = (xₐ - 21) fₐdₐ
18 184 -3 -552
19 212 -2 -424
20 327 -1 -327
21 = A 376 0 0
22 614 1 614
23 372 2 744
24 415 3 1245
∑fₐ = 2500 ∑fₐdₐ = 1300
∑fₐdₐ
Mean = (A + ---------)
∑fₐ
1300
= (21 + -------- )
2500
13
= (21 + -------) = 21 + 0.52 = 21.52
25
Hence the mean is 21.52 (Ans.)
Your second block of text...