Question

Following are the marks obtained by 10 students of a class. Calculate standard deviation and coefficient of standard deviation.

$\begin{array}{ccccccccccc}\text{Marks}& 12& 8& 17& 13& 15& 9& 18& 11& 6& 1\end{array}$

Answer 1

Calculation of Standard Deviation Using Direct Method

$\begin{array}{cccc}\text{S. No.}& \text{Marks}& \text{Deviation}& \text{Square of Deviation}\\ & \left(X\right)& (x=X-\overline{X})& x^2(=X-\overline{X}{)}^2\\ & & \overline{X}=11& \\ 1& 12& 12-11=1& 1\\ 2& 8& 8-11=-3& 9\\ 3& 17& 17-11=6& 36\\ 4& 13& 13-11=2& 4\\ 5& 15& 15-11=4& 16\\ 6& 9& 9-11=-2& 4\\ 7& 18& 18-11=7& 49\\ 8& 11& 11-11=0& 0\\ 9& 6& 6-11=-5& 25\\ 10& 1& 1-11=-10& 100\\ N=10& \sum X=110& \sum x=0& \sum x^2=244\end{array}$

$\overline{X}=\frac{\sum X}{N}=\frac{110}{10}=11$

$\sigma =\sqrt{\frac{\sum x^2}{N}}=\sqrt{\frac{244}{10}}=\sqrt{24.4}=4.94$

Coefficient of $SD=\frac{\sigma }{\overline{X}}=\frac{4.94}{11}=0.45$

SD = 4.94 marks, Coefficient of SD = 0.45