Question

Assume that a data set consists of only one outlier. If the outlier is removed, then which of the following measures of central tendency remains the same?

• A. Mean
• B. Mode
• C. Median
• D. None of the above

Answer 1

The correct option is B Mode

Let the number of gifts wrapped by Adam on different days of the week is given as follows:


The outlier is the value which is different from the other values of the data set. For the given data set, the outlier is $42$.

Arrange the given data in ascending order to find the different measures of central tendency in the presence of outlier.


The median for the even number of term is the average of the middle two terms. For the given data, the middle two values are $22$ and $24$, thus the median is given as,

$\begin{array}{cc}\text{Median}& =\frac{22+24}{2}\\ & =\frac{46}{2}\\ & =23\end{array}$

The mode is the most frequently occuring value in the given set, therefore for the given data, the mode is $22$.

The mean of the given data set is obtained as follows,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{21+22+22+24+25+42}{6}\\ & =\frac{156}{6}\\ & =26\end{array}$

Without outlier, the given data is represented as follows:


The median for odd number of terms is the middle value of the given data set. For the given data set, the median is $22$.

The mode is the most frequently occuring value in the given set, therefore for the given data, the mode is $22$.

The mean of the given data set is obtained as follows,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{21+22+22+24+25}{5}\\ & =\frac{114}{5}\\ & =22.8\end{array}$

Hence, it can be observed that for a data set with one outlier, only the value of mode remains same in the absence of outlier.