Question

Calculate Mean deviation from (i) arithmetic mean, (ii) Median:

Marks

:

7

4

10

9

15

12

7

9

7

Answer 1

Marks (X)	Deviation from Mean $D_{\overline{x}}=\left|X\mathit{-}\overline{X}\right|$	Deviation from Median DM =|X−M|
4	4.89	5
7	1.89	2
7	1.89	2
7	1.89	2
9	0.11	0
9	0.11	0
10	1.11	1
12	3.11	3
15	6.11	6
ΣX = 80	$\mathrm{\Sigma }\left|X\mathit{-}\overline{\mathit{X}}\right|=21.11$	Σ|X−Md| = 21

$$\begin{gathered} \overline{X}=\frac{\Sigma X}{N}=\frac{80}{9}=8.89 \\ \mathrm{Median}=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{9+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{5}^{\mathrm{th}}\mathrm{item} \\ =9 \\ \therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Mean}=\frac{{\displaystyle \left|X\mathit{-}\overline{X}\right|}}{N}=\frac{21.11}{9}=2.34 \\ \therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\left|X\mathit{-}{M}_{}\right|}{N}=\frac{21}{9}=2.32 \end{gathered}$$