Question

With respect to the impact of outlier on the measures of central tendency, choose the correct options.

• A. Mode of the data set may remain unaffected in the presence of outlier.
• B. Mean of the data set always changes in the presence of outlier.
• C. Mean with outlier is mean without outlier.
• D. Mode of the data set may vary in the absence of outlier.

Answer 1

Answer: (A), (B), (D)

Mode of the data set may vary in the absence of outlier.

Consider a data set which represents the number of sweaters sold in different months.


The outlier for this data is $9$ as this value is quite different from the remaining values of the data set.

The mean for this data set with and without outlier is calculated as,

$\begin{array}{cc}\text{Mean with outlier}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{38+36+35+9+9+31+39+36}{8}\\ & =\frac{233}{8}\\ & =29.12\\ & \\ \text{Mean without outlier}& =\frac{38+36+35+31+39+36}{6}\\ & =\frac{215}{6}\\ & =35.83\end{array}$

Thus, the outlier changes the value of the mean of the data set.

Now, observe the values in the data set that occur most frequently to obtain the mode.


It can be observed there are two numbers that occur frequently, i.e., $9$ and $36$, therefore the given data set in the presence of outlier is bimodal with values $9$ and $36$.

And in the absence of the outlier, the mode of this data set will be $36$.

Hence, the outlier may change the value of the mode of data.

Now consider another data set which depicts the age of a group of $6$ people.


The outlier for this data is $7$ because it is quite different from the rest of the data set.

Now, observe the values in the data set that occur most frequently in order to obtain the mode.


The most frequently occuring value in this data set is $20$, i.e., the mode of this data set is $20$ and it remains the same even in the absence of outlier.

Thus, for this data set the mode with outlier is the mode without outlier.

Hence, it can be concluded that the oultier always changes the value of mean of the data set but the mode of the data set may or may not change in the presence of outlier.