Question

Calculate the mean deviation from the mean for the data: 

 4, 7, 8, 9, 10, 12, 13, 17

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.

\[x = \frac{4 + 7 + 8 + 9 + 10 + 12 + 13 + 17}{8} = 10\]

\[x_i\]	\[\left| d_i \right| = \left| x_i - \bar{x} \right|\]
4	6
7	3
8	2
9	1
10	0
12	2
13	3
17	7
Total	24

 

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|\]

\[MD = \frac{1}{8} \times 24 = 3\]