Question

Calculate average of the following discrete series. Use Short-cut Method by taking 25 as assumed average.

Size	30	29	28	27	26	25	24	23	22	21
Frequency (f)	2	4	5	3	2	7	1	4	5	7

Answer 1

Size (X)	Frequency (f)	Deviation d = X − A	fd
30 29 28 27 26 25=A 24 23 22 21	2 4 5 3 2 7 1 4 5 7	5 4 3 2 1 0 −1 −2 −3 −4	10 16 15 6 2 0 −1 −8 −15 −28
	∑f = 40		∑fd = −3

A.M. = X=ΣXN =163010=163
Shortcut Method:-
Here, we take 25 as the assumed mean, so we tale the deviation of each item in the series from 25.
$\overline{X}=A+\frac{\Sigma fd}{\Sigma f}$
$$\begin{gathered} =25+\left(\frac{-3}{40}\right) \\ =25-0.075=24.925 \end{gathered}$$
Thus, the mean of the series is 24.925