Question

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?

• A. Ravi is more consistent and intelligent.
• B. Hashina is more consistent and intelligent.
• C. Ravi is more consistent and Hashina is more intelligent.
• D. Ravi is more intelligent and Hashina is more consistent.

Answer 1

Answer: (C)

Ravi is more consistent and Hashina is more intelligent.

Answer 2

For Ravi, let assumed mean = 45 $\sigma_{1}=\sqrt{\frac{\sum d_{i}^{2}}{n}-\left(\frac{\sum d_{i}}{n}\right)^{2}}$ $=\sqrt{\frac{1699}{10}-\left(\frac{-9}{10}\right)^{2}}$ $=\sqrt{169.9-0.81}=\sqrt{169.09}=13.00$ Now, mean $\left(\bar{x_{1}}\right)=\frac{\Sigma x_{i}}{n}=\frac{441}{10}=44.1$ For Hashina, let assumed mean = 55 $\sigma_{2}=\sqrt{\frac{5968}{10}-\left(\frac{-20}{10}\right)^{2}}=\sqrt{596.8-4}=\sqrt{592.8}=24.34$ Now, mean $\left(\bar{x}_{2}\right)=\frac{530}{10}=53$ For Ravi, $C.V._{1}=\frac{\sigma_{1}}{x_{1}}\times100=\frac{13}{44.1}\times100=29.47$ For Hashina, $C. V._{2}=\frac{\sigma_{2}}{\bar{x}_{2}}\times100=\frac{24.34}{53}\times100=45.92$ Hence, Ravi is more consistent and intelligent.