Question

Find the mean deviation from the mean for the data:

xi	10	30	50	70	90
fi	4	24	28	16	8

Answer 1

xi	fi	fi​xi	\[\left| x_i - \bar{x} \right|\]	\[f_i \left| x_i - 50 \right|\]
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
	\[N = 80\]	\[\sum^n_{i = 1} f_i x_i = 4000\]		\[\sum^n_{i = 1} f_i \left| x_i - 50 \right| = 1280\]

\[\bar{ x } = \frac{\sum ^n _{i = 1} f_ix_i}{N} = \frac{4000}{80} = 50\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i -\bar{ x } \right| = \frac{1}{80} \times 1280 = 16\]