Question

When a data set has an even number of elements, the median is calculated by __________. A. averaging the middle two values B. subtracting the middle two values C. eliminating any outliers and recalculating the median D. eliminating the smallest data value from the set and recalculating the median

Answer 1

When a data set has an even number of elements, the median is calculated by __________.

Answer: When the data set has an even number of elements, we find the median by averaging the middle two values. Therefore, the Option A. averaging the middle two values is correct.

Let's consider an example:

Suppose we have 8 observations and we are required to find the median.

The observations are:

$2,4,6,8,10,12,14,16$

Now to find the median, we first need to arrange the data in ascending order.

Then the median is:

$Median=\frac{4^{th} item +5^{th} item }{2}$

                    =$\frac{8+10}{2} =\frac{18}{2}=9$

Therefore, the median is 9, which is calculated by averaging the two middle values