# Following Are the Marks Obtained,Out of 100 by Two Students Ravi and Hashina in 10 Tests: - Mathematics

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

 Ravi: 25 50 45 30 70 42 36 48 35 60 Hashina: 10 70 50 20 95 55 42 60 48 80

Who is more intelligent and who is more consistent?

#### Solution

For Ravi

 Marks   $\left( x_i \right)$ $d_i = x_i - 45$ $d_i^2$ 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 $\sum_{} d_i = - 9$ $\sum_{} d_i^2 = 1699$
$X_R = A + \frac{\sum_{} d_i}{10} = 45 + \frac{\left( - 9 \right)}{10} = 44 . 1$
Standard deviation,
$\sigma_R = \sqrt{\frac{\sum_{} d_i^2}{10} - \left( \frac{\sum_{} d_i}{10} \right)^2} = \sqrt{\frac{1699}{10} - \left( \frac{- 9}{10} \right)^2} = \sqrt{169 . 09} = 13 . 003$
Coefficicent of variation = $\frac{\sigma_B}{X_B} \times 100 = \frac{110}{770} \times 100 = 14 . 29$
For Hashina
 Marks $\left( x_i \right)$ $d_i = x_i - 55$ $d_i^2$ 10 −45 2025 70 15 625 50 −5 25 20 −35 1225 95 40 1600 55 0 0 42 −13 169 60 5 25 48 −7 49 80 25 625 $\sum_{} d_i = - 20$ $\sum_{} d_i^2 = 6368$

Mean,

$X_H = A + \frac{\sum_{} d_i}{10} = 55 + \frac{\left( - 20 \right)}{10} = 53$
Standard deviation,
$\sigma_H = \sqrt{\frac{\sum_{} d_i^2}{10} - \left( \frac{\sum_{} d_i}{10} \right)^2} = \sqrt{\frac{6368}{10} - \left( \frac{- 20}{10} \right)^2} = \sqrt{632 . 8} = 25 . 16$
Coefficicent of variation = $\frac{\sigma_H}{X_H} \times 100 = \frac{25 . 16}{53} \times 100 = 47 . 47$
Since the coefficient of variation in mark obtained by Hashima is greater than the coefficient of variation in mark obtained by Ravi, so Hashina is more consistent and intelligent.
Concept: Statistics - Statistics Concept
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.7 | Q 12 | Page 49