Question

Calculate the mean deviation about the median of the observation:

 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

Answer 1

Formula used for mean deviation:

 

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

\[Here, \]

\[ d_i = x_i - M\]

 M = Median

iii) Arranging the data in ascending order:
30, 34, 38, 40, 42, 44, 50, 51, 60, 66

Here,

\[n = 10\]

Also, median is the AM of the fifth and the sixth observation.

\[Median, M = \frac{42 + 44}{2} = 43\]

xi	\[\left| d_i \right| = \left| x_i - M \right|\]
34	9
66	23
30	13
38	5
44	1
50	7
40	3
60	17
42	1
51	8
Total	87

\[MD = \frac{1}{10} \times 87 = 8 . 7\]