Question

Find the mean deviation from the mean for the data:

xi	5	10	15	20	25
fi	7	4	6	3	5

Answer 1

xi	fi	fixi	\[\left| x_i - \bar{x} \right|\]	\[f_i \left| x_i - 14 \right|\]
5	7	35	9	63
10	4	40	4	16
15	6	90	1	6
20	3	60	6	18
25	5	125	11	55
	\[N = 25\]	\[\sum^n_{i = 1} f_i x_i = 350\]		\[\sum^n_{i = 1} f_i \left| x_i - 14 \right| = 158\]

\[\bar { x  } = \frac{\sum^{n} _{i=l} f_i x_i}{N} = \frac{350}{25} = 14\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - x \right| = \frac{1}{25} \times 158 = 6 . 32\]