Q. 3.149 - Elementary Statistics

Question

Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.

Step-by-Step Solution

Answer

The advantage is that median and interquartile range are resistant to outliers.

Step 1: Given Information

We have to find out the advantage of median and interquartile range over the mean and standard deviation.

Step 2: Explanation

Firstly, take an example that you have$20$ students with their weight but one of the child weight is considered wrong it was taken $99$ but it was just $39$ then mean will have a huge difference  but median will be same which shows that median is not changed by outliers.

The standard deviation is more changed by outliers as it is the square of differences between sample values and mean but the interquartile range is not changed because like median it does not take extreme values.

Hence, the advantage of the median and interquartile range over the mean and standard deviation  is that they are not changed by outliers.