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Home » Following are the marks obtained, out of 100 , by two students Ravi and Hashina in 10 tests.     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?
CBSE | Class 11 | Maths | NCERT Exemplar | Statistics
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.

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