Question

Calculate the mean deviation about the median of the observation:

 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

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

iv) Arranging the data in ascending order.
22, 24, 25, 27, 28, 29, 30, 31, 41, 42

\[\text{ Here } , n = 10 .\]

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

\[Median, M = \frac{28 + 29}{2} = 28 . 5\]

xi	\[\left| d_i \right| = \left| x_i - M \right|\]
22	6.5
24	4.5
30	1.5
27	1.5
29	0.5
31	2.5
25	3.5
28	0.5
41	12.5
41	13.5
Total	47

 

\[MD = \frac{1}{10} \times 47 = 4 . 7\]