Question

Consider the following statement for a data set with more than two data points,

"The mean and median of the data set with even number of terms is same."

Is this statement correct?

• A. Yes
• B. No

Answer 1

The correct option is B No

Consider the following set of numbers,


The mean of the data set is,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{3+6+5+8+8+9}{6}\\ & =\frac{39}{6}\\ & =6.5\end{array}$

Now arrange the given set of numbers in ascending order.


Observe the two middle numbers and find their mean. The two middle numbers are $6$ and $8$ and hence their mean is,

$\begin{array}{cc}\text{Mean}& =\frac{6+8}{2}\\ & =\frac{14}{2}\\ & =7\end{array}$

Thus, the median of the given set of numbers is $7$.

Hence, the mean of the given set of numbers is not same as the median of the set of numbers.

So, the given statement is wrong.