Question

Adam played $7$ games and recorded the data of his scores as follows:


What is the difference between the mean in the presence and absence of outlier?

• A. $12.8$
• B. $-2.7$
• C. $-6.2$
• D. $93$

Answer 1

The correct option is A $12.8$

Observe the given data,


All the values of this data set lies within the range of $197$ to $207$, except the value $290$ which is quite larger from the rest of the values.
Thus, by definition of oultlier, $290$ is said to be the outlier of this data set.

The mean of the data set is calculated as,

$\text{Mean}=\frac{\text{Sum of all data points}}{\text{Total number of data points}}$

The mean with and without the presence of outlier will be given as,

$\begin{array}{cc}\text{Mean with outlier}& =\frac{198+197+200+205+290+198+207}{7}\\ & =\frac{1495}{7}\\ & =213.6\\ & \\ \text{Mean without outlier}& =\frac{198+197+200+205+198+207}{6}\\ & =\frac{1205}{6}\\ & =200.8\end{array}$

Thus, the difference between the mean with and without outlier is calculated as,

$\begin{array}{cc}\text{Required difference}& =\text{Mean with outlier}-\text{Mean without outlier}\\ & =213.6-200.8\\ & =12.8\end{array}$