Question

Calculate range, standard deviation and coefficient of variation of marks secured by students.

50

55

57

49

54

61

64

59

58

56

Answer 1

X	$x\mathit{=}\left(\mathit{X}\mathit{-}\overline{\mathit{X}}\right)$	x2
50 55 57 49 54 61 64 59 58 56	−6.3 −1.3 .7 −7.3 −2.3 4.7 7.7 2.7 1.7 −.3	39.69 1.69 .49 53.29 5.29 22.09 59.29 7.29 2.89 .09
$\sum _{}^{}X=563$		$\sum _{}^{}{x}^2=192.1$

Here,
N = 10
Highest value (H) = 64
Lowest value (Z) = 49
Range (R) = H − L = 64 − 49 = 15
So, range is 15.
$$\begin{gathered} \mathrm{Mean}\left(\overline{X}\right)=\frac{{\sum }_{}X}{N}=\frac{563}{10}=56.3 \\ \mathrm{Standard}\mathrm{Deviation}\left(\sigma \right)=\sqrt{\frac{{\sum }_{}{x}^2}{N}}=\sqrt{\frac{192.1}{10}}=4.38 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Variation}=\frac{\sigma }{\overline{X}}\times 100=\frac{4.38}{56.3}\times 100=7.78 \end{gathered}$$