Question

A set of $6$ numbers is represented as follow:


If $96$ is added to this set of numbers, then what will the impact of this new number on mean?

• A. The mean will decrease.
• B. The mean will remain the same.
• C. The mean will increase.
• D. Cannot be determined

Answer 1

The correct option is C The mean will increase.

The mean of the given data will be calculated as,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all the data points}}{\text{Total number of data points}}\\ & =\frac{36+39+37+34+37+33}{6}\\ & =\frac{216}{6}\\ & =36\end{array}$

Now, when $96$ is added to the given data, it will be represented as


The number $96$ which is being added to the given data set is an outlier as it lies beyond the range of the given numbers. Thus, the mean in the presence of outlier will be,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all the data points}}{\text{Total number of data points}}\\ & =\frac{36+39+37+34+37+33+96}{7}\\ & =\frac{312}{7}\\ & =44.57\end{array}$

Hence, the mean of the given data will increase in the presence of outlier.

So, option (c) is correct.