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The Mean and Standard Deviation of Marks Obtained by 50 Students of a Class in Three Subjects, Mathematics, Physics and Chemistry Are Given Below:

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Question

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, physics and chemistry are given below: 

Subject Mathematics Physics Chemistry
Mean 42 32 40.9
Standard Deviation 12 15 20

Which of the three subjects shows the highest variability in marks and which shows the lowest?

 
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Solution

We know: \[CV = \frac{\sigma}{\bar{X}} \times 100\]

\[\bar{{X_m}} = 42, \sigma_m = 12\]

\[ \bar{{X_p}} = 32, \sigma_p = 15\]

\[ \bar{{X_c}} = 40 . 9, \sigma_c = 20\]

CV of mathematics marks 

\[= \frac{12}{42} \times 100 = \frac{1200}{42} = 28 . 57\]
CV of physics marks ​
 
\[= \frac{15}{32} \times 100 = \frac{1500}{32} = 46 . 87\]
CV of chemistry marks  \[= \frac{20}{40 . 9} \times 100 = \frac{2000}{40 . 9} = 48 . 89\]

Since CV of chemistry is the greatest, the variability of marks in chemistry is the highest and that of mathematics is the lowest.

 
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Chapter 32: Statistics - Exercise 32.7 [Page 48]

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R.D. Sharma Mathematics [English] Class 11
Chapter 32 Statistics
Exercise 32.7 | Q 7 | Page 48

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