Question

Determine whether the given statement is true or false.

"The median is always one of the values given in the data set."

• A. False
• B. True

Answer 1

The correct option is A False

Let us consider two cases.

Case I: The data set with odd number of terms.

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

For example, consider the following set of numbers,


It can be observed that the numbers are already in ascending order and the middle number is $9$. Thus, the median for this set of odd number of terms is $9$.

Case II: The data set with even number of terms.

For even number of terms, the median is obtained by following two steps as:

Step I: Arrange the given set in ascending order.

Step II: Find the average of the middle two terms.

For example, consider the following set of $6$ numbers,


Since the set is already in ascending order and the middle two numbers are $8$ and $9$, therefore the median of this data set is calculated as,

$\begin{array}{cc}\text{Median}& =\frac{8+9}{2}\\ & =\frac{17}{2}\\ & =8.5\end{array}$

Thus, for even number of terms, the median may not be one of the values given in the data set.

Hence, it can be concluded that the median is not always the one of the values of the data set.

So, the given statement is false.