Question

Given below are the marks obtained by the students of a class. Calculate mean deviation, and its coefficient, using median of data.

Marks

17

35

38

16

42

27

19

11

40

25

Answer 1

The given data is an individual series, therefore, to calculate median, we first need to arrange the data in ascending order. This is done as below.

$$\begin{gathered} \mathrm{11,\; 16,}\mathrm{17,}\mathrm{19,}\boxed{25},\boxed{27},\mathrm{35,}\mathrm{38,}\mathrm{40,}42 \\ \mathrm{Here,}N=10\left(\mathit{e}\mathit{v}\mathit{e}\mathit{n}\right) \\ \mathrm{Median}=\frac{\mathrm{size}\mathrm{of}{\left(\frac{N}{2}\right)}^{th}\mathrm{item}+\mathrm{size}\mathrm{of}{\left(\frac{N}{2}+1\right)}^{th}\mathrm{item}}{2} \\ \mathrm{or},\mathrm{Median}=\frac{\mathrm{size}\mathrm{of}{5}^{th}\mathrm{item}+\mathrm{size}\mathrm{of}{6}^{th}\mathrm{item}}{2}=\frac{25+27}{2}=26 \\ \mathrm{so},\mathrm{Median}\mathrm{is}26. \end{gathered}$$
Thus, we calculate the deviation of values from 26

X	|x - M| = |dM|
11 16 17 19 25 27 35 38 40 42	15 10 9 7 1 1 9 12 14 16
	∑|dM| = 94

$$\begin{gathered} \mathrm{Mean}\mathrm{Deviation}\mathrm{from}\mathrm{Median}\mathit{}\left(M{D}_M\right)=\frac{{\sum }_{}\left|d_M\right|}{n}=\frac{94}{10}=9.4 \\ C\mathrm{oefficient}\mathrm{of}M{D}_M=\frac{M{D}_M}{Median}=\frac{9.4}{26}=0.36 \end{gathered}$$