Question

With reference to the impact of outlier on mean, which of the following option is correct?

• A. The value of mean remains unaffected with or without outlier.
• B. The presence of outlier may increase or decrease the value of mean.
• C. The presence of outlier in the data set always increases its mean.
• D. None of the above.

Answer 1

The correct option is B The presence of outlier may increase or decrease the value of mean.

Consider the data set for the number of states visited by students as follows:


In the given data, all the values lies within the range of $0$ to $6$, except for $18$ which is quite different from the other values. Thus, $18$ is said to be the outlier of this data set.

The mean of this data is calculated as,

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

Thus, the mean with and without outlier will be given as,

$\begin{array}{cc}\text{Mean with outlier}& =\frac{4+3+6+2+0+3+4+6+5+5+4+18+1+2}{14}\\ & =\frac{63}{14}\\ & =4.5\\ & \\ \text{Mean without outlier}& =\frac{4+3+6+2+0+3+4+6+5+5+4+1+2}{13}\\ & =\frac{45}{13}\\ & =3.5\end{array}$

Hence for this data set, the presence of outlier increases the value of mean.

Now, consider another data set showing the age of $5$ people.


In this data set, all the values lies within $34$ to $36$, except for $12$ which is quite different from the range of other values. Thus, $12$ is said to be the outlier of this data set.

Here, the mean with and without outlier will be given as,

$\begin{array}{cc}\text{Mean with outlier}& =\frac{34+33+12+35+36}{5}\\ & =\frac{150}{5}\\ & =30\\ & \\ \text{Mean without outlier}& =\frac{34+33+35+36}{4}\\ & =\frac{138}{4}\\ & =34.5\end{array}$

Hence for this data set, the presence of outlier decreases the value of mean.

Thus, the presence of outlier may increase or decrease the value of the mean of a given data set.