Following are the marks obtained, out of 100 , by two students Ravi and Hashina in 10 tests. $$\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline Ravi & 25 & 50 & 45 & 30 & 70 & 42 & 36 & 48 & 35 & 60 \\ \hline Hashina & 10 & 70 & 50 & 20 & 95 & 55 & 42 & 60 & 48 & 80 \\ \hline \end{tabular}$$ Who is more intelligent and who is more consistent?
Following are the marks obtained, out of 100 , by two students Ravi and Hashina in 10 tests. $$\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline Ravi & 25 & 50 & 45 & 30 & 70 & 42 & 36 & 48 & 35 & 60 \\ \hline Hashina & 10 & 70 & 50 & 20 & 95 & 55 & 42 & 60 & 48 & 80 \\ \hline \end{tabular}$$ Who is more intelligent and who is more consistent?

Solution:

For Ravi

$$\begin{tabular}{|c|c|c|}
\hline$x_{i}$ & $d_{i}=x_{i}-45$ & $d_{i}^{2}$ \\
\hline 25 & $-20$ & 400 \\
\hline 50 & 5 & 25 \\
\hline 45 & 0 & 0 \\
\hline 30 & $-15$ & 225 \\
\hline 70 & 25 & 625 \\
\hline 42 & $-3$ & 9 \\
\hline 36 & $-9$ & 81 \\
\hline
\end{tabular}$$

$$\begin{tabular}{|c|r|r|}
\hline 48 & 3 & 9 \\
\hline 35 & $-10$ & 100 \\
\hline 60 & 15 & 225 \\
\hline Total & $\Sigma d_{i}=-9$ & $\Sigma d^{2} i=1699$ \\
\hline
\end{tabular}$$

$\begin{aligned}
\sigma &=\sqrt{\frac{\Sigma d_{i}^{2}}{n}-\left(\frac{\Sigma d_{i}}{n}\right)^{2}}=\sqrt{\frac{1699}{10}-\left(\frac{-9}{10}\right)^{2}} \\
&=\sqrt{169.9-0.81}=\sqrt{169.09}=13.003
\end{aligned}$

So now, $\quad \bar{x}=A+\frac{\Sigma d_{i}}{\Sigma f_{i}}=45-\frac{14}{10}=43.6$
For Hashina,

$$\begin{tabular}{|c|c|c|}
\hline $\boldsymbol{x}_{\boldsymbol{i}}$ & $\boldsymbol{d}_{i}=\boldsymbol{x}_{\boldsymbol{i}}-\mathbf{5 5}$ & $\boldsymbol{d}_{i}^{2}$ \\
\hline 10 & $-45$ & 2025 \\
\hline 70 & 15 & 225 \\
\hline 50 & $-5$ & 25 \\
\hline 20 & $-35$ & 1225 \\
\hline 95 & 40 & 1600 \\
\hline 55 & 0 & 0 \\
\hline 42 & $-13$ & 169 \\
\hline 60 & 5 & 25 \\
\hline 48 & $-7$ & 49 \\
\hline 80 & 25 & 625 \\
\hline Total & $\Sigma d_{i}=-20$ & $\Sigma d^{2} i=5968$ \\
\hline
\end{tabular}$$

$\therefore \quad \sigma=\sqrt{\frac{5968}{10}-\left(\frac{-20}{10}\right)^{2}}=\sqrt{596.8-4}=\sqrt{592.8}=24.46$

For Ravi, $\mathrm{CV}=\frac{\sigma}{\bar{x}} \times 100=\frac{13.003}{43.6} \times 100=29.82$

For Hashina, $\mathrm{CV}=\frac{\sigma}{\bar{x}} \times 100=\frac{24.46}{55} \times 100=44.47$

As a result, Hashina is more consistent and intelligent.