Question

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests :

$\begin{array}{ccccccccccc}\text{Ravi :}& 25& 50& 45& 30& 70& 42& 36& 48& 35& 60\\ \text{Hashina :}& 10& 70& 50& 20& 95& 55& 42& 60& 48& 80\end{array}$

Who is more intelligent and who is more consistent ?

Answer 1

For Ravi,

$\begin{array}{ccc}{x}_i& d_i=x_i-45& d_i^2\\ 25& -20& 400\\ 50& 5& 25\\ 45& 0& 0\\ 30& -15& 225\\ 70& 25& 625\\ 42& -3& 9\\ 36& -9& 81\\ 48& 3& 9\\ 35& -10& 100\\ 60& 15& 225\\ Total& \sum d_i=-14& \sum d_i^2=1699\end{array}$

$\sigma =\sqrt{\frac{\sum d_i^2}{n}-{\left(\frac{\sum d_i}{n}\right)}^2}=\sqrt{\frac{1699}{10}-{\left(\frac{-14}{10}\right)}^2}=\sqrt{169.9-0.0196}$

$=\sqrt{169.88}=13.03$

Now,

For Hashina :

$\begin{array}{ccc}{x}_i& d_i=x_i-45& d_i^2\\ 10& -45& 2025\\ 70& 25& 625\\ 50& -5& 25\\ 20& -35& 1225\\ 95& 40& 1600\\ 55& 0& 0\\ 42& -13& 169\\ 60& 5& 25\\ 48& -7& 49\\ 80& 25& 625\\ Total& \sum d_i=0& \sum d_i^2=6368\end{array}$

$\because$ Mean = 55

$\Rightarrow \sigma =\sqrt{\frac{6368}{10}}=\sqrt{6368}=25.2$

For Ravi, CV = $\frac{\sigma }{\overline{x}}\times 100=\frac{13.03}{43.6}\times 100=29.88$

For Hashina , $\frac{\sigma }{\overline{x}}\times 100=\frac{25.2}{55}\times 100=45.89$

Hence, Hashina is more consistent and intelligent.