Question

Calculate the mean deviation about the median of the observation:

 38, 70, 48, 34, 63, 42, 55, 44, 53, 47

 

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

v) Arranging the data in ascending order:
34, 38, 42, 44, 47, 48, 53, 55, 63, 70

Here,

\[n = 10\].

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

\[Median, M = \frac{47 + 48}{2} = 47 . 5\]

xi	\[\left| d_i \right| = \left| x_i - M \right|\]
38	9.5
70	22.5
48	0.5
34	13.5
63	15.5
42	5.5
55	7.5
44	3.5
53	5.5
47	0.5
Total	84

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