Question

Find the mean deviation from the mean for the data:

Size	20	21	22	23	24
Frequency	6	4	5	1	4

Answer 1

Size(xi)	Frequency (fi)	fi​xi	\[\left| x_i - \bar{x} \right|\] \[ = \left| x_i - 21 . 65 \right|\]	\[f_i \left| x_i - x \right|\] \[ = f_i \left| x_i - 21 . 65 \right|\]
20	6	120	1.65	9.9
21	4	84	0.65	2.6
22	5	110	0.35	1.75
23	1	23	1.35	1.35
24	4	96	2.35	9.4
	\[N = 20\]	\[\sum^n_{i = 1} f_i x_i = 433\]		\[\sum^n_{i = 1} f_i \left| x_i - x \right| = 25\]

\[\bar{x} = \frac{\sum^{n}_{i = 1} f_ix_i}{N} = \frac{433}{20} = 21 . 65\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - x \right| = \frac{1}{20} \times 25 = 1 . 25\]