Question

In the final examination of statistics the mean marks of the group of 150 students were 78 and the s.d was 8.0. In Economics, however, the mean marks were 73 and the s.d was 7.6. The variance in the two subjects respectively is
A. 10.3%, 10.4%
B. 95%, 9.7%
C. 11.2%, 10.1%
D. None of these

Answer 1

Hint: Whenever we have asked for variability, certain concepts should come in our mind. The correlation coefficient, coefficient of variance are the two topmost concepts for the same.
Since we have given mean and standard deviation for both the subject i.e. statistics and economics so we’ll use the formula for the coefficient of variance to get the required answer.

Complete step by step answer:
We know the formula for the coefficient of variance as $\dfrac{\sigma }{{\overline x }} \times 100$. Where $\sigma $ represents the standard deviation and $\overline x $ represents the mean of x.
We’ll calculate the coefficient of variance for both the subjects one by one.
Statistics:
coefficient of variance= $\dfrac{8}{{78}} \times 100$
Which is nothing but 10.3%
Now, we’ll calculate the coefficient of variance for economics
$
  \dfrac{\sigma }{{\overline x }} \times 100 \\
   \Rightarrow \dfrac{{7.6}}{{73}} \times 100 \\
$
Which is equal to 10.4%
Hence, Option A is the correct option.
Note:
The coefficient of variance gives us the percentage amount of data that varies or deviates from the mean. Since it varies from the mean that is why it is called variance. The correlation coefficient is also a similar concept but it tells us the relation between two random variables.