Question

Find the mean deviation about the mean for the data

\(x_i\)	10	30	50	70	90
\(f_i\)	4	24	28	16	8

Answer 1

\(x_i\)	\(f_i\)	\(f_ix_i\)	\(|x_i-\bar{x}|\)	\(f_i|x_i-\bar{x}|\)
10	4	40	40	160
30	24	720	20	480
50	28	1400	0	0
70	16	1120	20	320
90	8	720	40	320
	80	4000		1280

\(N=\sum_{I=1}^{5}f_i=80\)  \(\sum_{I=1}^{5}f_i=4000\)

∴ \(\bar{x}=\frac{1}{N}\sum_{I=1}^{5}f_ix_i=\frac{1}{80}X4000=50\)

\(MD(\bar{x})=\frac{1}{N}\sum_{i=1}^{5}f_i|x_i-\bar{x}|=\frac{1}{80}×1280= 16\)