Question

Calculate the mean deviation from the mean for the  data:

 38, 70, 48, 40, 42, 55, 63, 46, 54, 44a

Answer 1

Formula used for finding the mean deviation about the mean is given below: 

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right| , \text{ where } \left| d_i \right| = \left| x_i - x \right|\]

Let x  be the mean of the given data.

\[x = \frac{38 + 70 + 48 + 40 + 42 + 55 + 63 + 46 + 54 + 44}{10} = 50\]

\[x_i\]	\[\left| d_i \right| = \left| x_i - \bar{x} \right|\]
38	12
70	20
48	2
40	10
42	8
55	5
63	13
46	4
54	4
44	6
Total	84

 

\[MD = \frac{1}{10} \times 84 = 8 . 4\]