Question

The mean and S.D 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 lowest coefficient of variation?

Answer 1

The coefficient of variation is given by the formula $CV = \dfrac{{SD}}{{mean}} \times 100$, where SD is the standard deviation and the mean is the average of all the data. CV is the coefficient of variation of the data set whose mean and standard deviation is given for different subjects.

Complete step-by-step answer:
In the question, it is given that the mean and S.D of marks obtained by 50 students of a class in three subjects, mathematics, physics, and chemistry are as follows:

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

Now, we have to find the subject with the lowest coefficient of variation. So here we know that the higher the coefficient of variation, the more is the deviation from the mean of the data. The standard deviation is the measure that gives the percentage of data that lies around the mean. Also, we know that the mean is the average of the data given.
Now the formula that we use to find the coefficient of variation is given as:
$CV = \dfrac{{SD}}{{mean}} \times 100$
where SD is the standard deviation and the mean is the average of all the data. CV is the coefficient of variation.
Substitute the values in the formula to find the coefficient of variation for Mathematics,
$\Rightarrow CV = \dfrac{{12}}{{42}} \times 100$
Multiply the terms of the numerator with 100,
$\Rightarrow CV = \dfrac{{1200}}{{42}}$
Divide the numerator by denominator,
$\Rightarrow CV = 28.57$
Substitute the values in the formula to find the coefficient of variation for Physics,
$\Rightarrow CV = \dfrac{{15}}{{32}} \times 100$
Multiply the terms of the numerator with 100,
$\Rightarrow CV = \dfrac{{1500}}{{32}}$
Divide the numerator by denominator,
$\Rightarrow CV = 46.875$
Substitute the values in the formula to find the coefficient of variation for Chemistry,
$\Rightarrow CV = \dfrac{{20}}{{40.9}} \times 100$
Multiply the terms of the numerator with 100,
$\Rightarrow CV = \dfrac{{2000}}{{40.9}}$
Divide the numerator by denominator,
$\Rightarrow CV = 48.89$
So now, we can see that the lowest coefficient of variation is $28.57$.

Hence, Mathematics shows the lowest coefficient of variation.

Note: It can be noted that the coefficient of variation is very different from the variance. The variance is square of standard deviation, S.D. Also, be careful to multiply the ratio $\dfrac{{SD}}{{mean}}$ by 100 when we are finding the coefficient of variation.