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?
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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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