Question

Calculate the mean deviation about the median of the observation:

 38, 70, 48, 34, 42, 55, 63, 46, 54, 44

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

ii) Arranging the data in ascending order:
34, 38, 42, 44, 46, 48, 54, 55, 63, 70

Here, n is equal to 10.
Median is the arithmetic mean of the fifth and the sixth observation.

\[Median, M = \frac{46 + 48}{2} = 47\]

xi	\[\left| d_i \right| = \left| x_i - M \right|\]
38	9
70	23
48	1
34	13
42	5
55	8
63	16
46	1
54	7
44	3
Total	86

\[MD = \frac{1}{10} \times 86 = 8 . 6\]