Question

The sale of chocolates is recorded for a week and is represented as follows:


Find the outlier and the change observed in the median in the absence of outliner.

• A. 57; the median will increase.
• B. 27; the median will decrease.
• C. 57; the median will decrease.
• D. 27; the median will increase.

Answer 1

The correct option is C 57; the median will decrease.

The outlier is that value in the given data which is quite different from the rest of the values.

Thus, for the given data, the outlier is $57$ as it does not lie within the range of other values.

The median of the given data set with odd number of terms is the middle value when the data is arranged in ascending order.
Since the given data is already in ascending order, therefore the middle term is $36$.


Thus, the median of the data set with outlier is $36$.

Now, observe the data without outlier.


For even number of terms, the median is the average of middle two terms, that are, $32$ and $36$, which is calculated as,

$\begin{array}{cc}\text{Average}& =\frac{32+36}{2}\\ & =\frac{68}{2}\\ & =34\end{array}$

Thus, the median without outlier is $34$.

Hence, the outlier of the given data is $57$ and in its absence the median decreases.