Question

A distribution has mean $ = 8.7 $ , median $ = 8.5 $ and mode $ = 7.3 $ . The distribution is:
A.Positively skewed
B.Negatively skewed
C.Symmetrical
D.None of these

Answer 1

Hint: Check the relation between all the mean, median and mode with given values to check the nature of the given distribution whether the distribution is positive/ negative skewed or symmetrical or not.

Complete step-by-step answer:
As given in the question that the distribution is such that the mean is equal to $ 8.7 $ , median is equal to $ 8.5 $ and mode is equal to $ 7.3 $ .
Now as it is visible from the values only that in the given distribution the mean value is greater than the median value and the median value is greater than the mode value. So, the mean value is greatest among all.
A relation between all the three can be written as $ {\text{mean}} > {\text{median}} > {\text{mode}} $ .
In this case, the distribution is always positively skewed or we can say that the distribution is skewed right.
Hence option (A) is the correct answer.
So, the correct answer is “Option A”.

Note: The three cases for the nature of distribution is given below:
If $ {\text{mean}} = {\text{median}} = {\text{mode}} $ , then the skewness is always $ 0 $ i.e. the shape of the distribution is symmetric.
If $ {\text{mean}} > {\text{median}} > {\text{mode}} $ , then the skewness is positive i.e. the distribution is skewed right.
If $ {\text{mean}} < {\text{median}} $ , then the skewness is negative i.e. the distribution is skewed left.