Question

Calculate the Mean Deviation from mean and median of the following data:

X

:

54

71

57

52

49

45

72

57

47

Answer 1

X	Deviation from Median DM =|X−M| M = 54	Deviation from Mean $D_{\overline{X}}=\left|X-\overline{X}\right|$ $\overline{X}=56$
45	9	11
47	7	9
49	5	7
52	2	4
54	0	2
57	3	1
57	3	1
71	17	15
72	18	16
ΣX = 504	Σ|X−Md| = 64	$\mathrm{\Sigma }\left|X\mathit{-}\overline{\mathit{X}}\right|=66$

$$\begin{gathered} \mathrm{Median}=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{2}\right)}^{\mathrm{th}}\mathrm{item}={\left(\frac{9+1}{2}\right)}^{\mathrm{th}}=5^{\mathrm{th}}\mathrm{item}=54 \\ \mathrm{Mean}=\frac{\mathit{\Sigma }\mathit{X}}{\mathit{N}}=\frac{504}{9}=56 \end{gathered}$$
$$\begin{gathered} \therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Mean}=\frac{\mathrm{\Sigma }\mathit{}\left|X\mathit{-}\overline{X}\right|}{N}=\frac{66}{9}=7.33 \\ \therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\mathrm{\Sigma }\left|X\mathit{-}M\right|}{N}=\frac{64}{9}=7.11 \end{gathered}$$