Question

Find the mean deviation from the mean for the data:

xi	5	7	9	10	12	15
fi	8	6	2	2	2	6

Answer 1

 

xi	fi	fixi	\[\left| x_i - \bar{x} \right|\]	\[f_i \left| x_i - 9 \right|\]
5	8	40	4	32
7	6	42	2	12
9	2	18	0	0
10	2	20	1	2
12	2	24	3	6
15	6	90	6	36
	\[N = \Sigma f_i = 26\]	\[\sum^n_{i = 1} f_i x_i = 234\]		\[\sum^n_{i = 1} f_i \left| x_i - 9 \right| = 88\]

\[x = \frac{\sum f_in_{i = 1} x_i}{N} = \frac{234}{26} = 9\]

\[M . D . = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - x \right| = \frac{1}{26} \times 88 = 3 . 39\]