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:

The standard deviation of mathematics = 12

The standard deviation of Physics = 15

The standard deviation of Chemistry = 20

The coefficient of variation (C.V) is given by standard deviation/mean × 100

C.V (Mathematics)

= 12/42 × 100

= 28.57

C.V (Physics)

= 15/32 × 100

= 46.87

C.V (Chemistry)

= 20/40.9 x 100

= 48.89

The subject with greater C.V is more variable than others.

Therefore,

the highest variability in marks is in Chemistry and the lowest variability in marks is in Mathematics

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NCERT Solutions Class 11 Maths Chapter 15 Exercise ME Question 6

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below: Which of the three subjects shows the highest variability in marks and which shows the lowest?

Summary:

From the given data, the highest variability in marks is in chemistry and the lowest variability in marks is in mathematics