Question

Calculate the mean deviation from the mean for the  data:

 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 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. 

\[x = \frac{13 + 17 + 16 + 14 + 11 + 13 + 10 + 16 + 11 + 18 + 12 + 17}{12} = 14\]

\[x_i\]	\[\left| d_i \right| = \left| x_i - \bar{x} \right|\]
13	1
17	3
16	2
14	0
11	3
13	1
10	4
16	2
11	3
18	4
12	2
17	3
Total	28

 

\[MD = \frac{1}{12} \times 28 = 2.33\]