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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: - Mathematics

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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?

 

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

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