Question

Calculate the mean deviation about the mean for the following frequency distribution:
 

Class interval:	0–4	4–8	8–12	12–16	16–20
Frequency	4	6	8	5	2

Answer 1

Let the assumed mean A = 10 and h = 4. 

Class Interval	Mid-Value(xi)	Frequency(fi)	\[d_i = \frac{x_i - 10}{4}\]	\[f_i d_i\]	\[\left| x_i - X \right|\] \[ = \left| x_i - 9 . 2 \right|\]	\[f_i \left| x_i - X \right|\]
0–4	2	4	−2	−8	7.2	28.8
4–8	6	6	−1	−6	3.2	19.2
8–12	10	8	0	0	0.8	6.4
12–16	14	5	1	5	4.8	24
16–20	18	2	2	4	8.8	17.6
		N = 25		\[\sum f_i d_i\]=-5		\[\sum f_i |x_i-\bar{x}|=96\]

Here, N = 25 and

\[\sum f_i d_i\]=-5

Mean,

 

\[X = A + h\left( \frac{1}{N} \sum_{} f_i d_i \right)\]
\[ = 10 + 4\left( \frac{1}{25} \times \left( - 5 \right) \right)\]
\[ = 10 - \frac{20}{25}\]
\[ = 10 - 0 . 8\]
\[ = 9 . 2\]

∴ Mean deviation about mean

\[= \frac{1}{N}\sum_{} f_i \left| x_i - X \right| = \frac{1}{25} \times 96 = 3 . 84\]