Question

Calculate the Mean deviation from median of the following data:

Marks

:

41

66

59

38

54

21

32

49

68

Answer 1

Marks (X)	Deviation from Median D= |X−M| (M = 49)
21	28
32	17
38	11
41	8
49	0
54	5
59	10
66	17
68	19
	ΣD = 115

For the calculation of mean deviation, the given data is first arranged in the ascending order as done above. Then median is calculated in the following manner.
$$\begin{gathered} \mathrm{Median}=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{9+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{5}^{\mathrm{th}}\mathrm{item} \\ =49 \\ \therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\Sigma D}{N}=\frac{115}{9}=12.77 \end{gathered}$$
Thus, mean deviation from median is 12.77.