Question

Find the mean deviation from the mean for the data:

Size	1	3	5	7	9	11	13	15
Frequency	3	3	4	14	7	4	3	4

Answer 1

 

Size(xi)	Frequency (fi)	fi​xi	\[\left| x_i - \bar{x} \right|\] \[ = \left| x_i - 8 \right|\]	\[f_i \left| x_i - x \right|\] \[ = f_i \left| x_i - 8 \right|\]
1	3	3	7	21
3	3	9	5	15
5	4	20	3	12
7	14	98	1	14
9	7	63	1	7
11	4	44	3	12
13	3	39	5	15
15	4	60	7	28
	\[N = 42\]	\[\sum^n_{i = 1} f_i x_i = 336\]		\[\sum^n_{i = 1} f_i \left| x_i - x \right| = 124\]

\[\bar{x} = \frac{\sum ^n_{i = 1} f_ix_i}{N} = \frac{336}{42} = 8\]

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| x_i - x \right| = \frac{1}{42} \times 124 = 2 . 95\]