Question

# Calculate the Mean Deviation from mean and median of the following data: X : 54 71 57 52 49 45 72 57 47

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Solution

## 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 $\mathrm{\Sigma }\left|X\mathit{-}\overline{)\mathit{X}}\right|=66$ $\mathrm{Median}=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{2}\right)}^{\mathrm{th}}\mathrm{item}={\left(\frac{9+1}{2}\right)}^{\mathrm{th}}={5}^{\mathrm{th}}\mathrm{item}=54\phantom{\rule{0ex}{0ex}}\mathrm{Mean}=\frac{\mathit{\Sigma }\mathit{X}}{\mathit{N}}=\frac{504}{9}=56$ $\therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Mean}=\frac{\mathrm{\Sigma }\mathit{}\left|X\mathit{-}\overline{)X}\right|}{N}=\frac{66}{9}=7.33\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\mathrm{\Sigma }\left|X\mathit{-}M\right|}{N}=\frac{64}{9}=7.11$

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