Question

Jack's scores in different games is represented as follows:


Find the impact of outlier on the median and mode of this data.

• A. Mode remains same, while median decreases in the absence of outlier.
• B. Both mode and median increases in the absence of outlier.
• C. Median remains same, while mode decreases in the presence of outlier.
• D. Both mode and median remains same in the presence of outlier.

Answer 1

The correct option is D Both mode and median remains same in the presence of outlier.

The oultier of the data set is that value which is quite different from the rest of the values.

Observe the given data set,


Here, $19$ is beyond the range of the remaining values, therefore the outlier of this data set is $19$.

The median of the data set with odd number of terms is the middle number after arranging the data set in ascending order.

To calculate the median of the data set with outlier, arrange it in ascending order.


The middle two numbers are $6$ and $6$, thus the median of this data is computed as,

$\begin{array}{cc}\text{Median with outlier}& =\text{Mean of 6 and 6}\\ & =\frac{6+6}{2}\\ & =\frac{12}{2}\\ & =6\end{array}$

Moreover, the mode of the data set with outlier is $6$ as it is the most frequently occuring number.

Now, observe the data set without outlier.


Since the number of values in the data set is odd, therefore the median is the middle number which is $6$.

Thus, the median without outlier is $6$.

Furthermore, the mode without outlier is $6$, as it can be observed from the following data set,


Hence, it can be concluded that for the givcen data set, the mode and median remains same in the presence and absence of outlier.

So, option (d) is correct.