This tutorial will cover the range and the interquartile range. You’ll learn about:
Range and interquartile range are similar ideas in that they're both actually measured by subtraction, so they're not particularly difficult to calculate.
Range
The difference between the largest and smallest number in a data set.
Interquartile Range
The difference between the third and first quartiles. It represents the range in which the middle 50% of the data points lie.
While they are calculated similarly, they do measure different measures of variation.
This chart shows the height of the Chicago Bulls basketball team for a particular year:
It's easy to see from the list that the minimum value is 71 and the maximum value is 84.
The range is actually the easiest measure of spread or variation to find: take the maximum value (in this case, the tallest person) and subtract the minimum value (in this case, the shortest person). 84-71=13 inches. This means that every individual on the team falls within a 13 inch range.
The interquartile range is another measure of spread, but it's median based. To review, the median is the middle number of an ordered data set. Finding the median takes a few steps:
The three numbers are called:
The interquartile range, also abbreviated IQR, is the difference between the two quartiles.
This means that half, the middle half, of the data set falls within a 7 inch range, whereas the entire data set falls within a 13 inch range.
Visually, the IQR is the box on a box plot.
The range gives the entire spread of the data set lowest to highest whereas the IQR gives the range of the middle 50%.
The advantage of using IQR over range is if there are outliers, which would disproportionately affect the range, the IQR will not be affected by them.
The range is not the most useful measure of variation but it is the easiest to calculate. The interquartile range is more useful and measures the range of the middle 50%, the most typical middle 50% of the data. It's a useful measure of spread for distributions with outliers or skewness. In fact, you should use IQR as your measure of variation when there are outliers or skewness.
Because the IQR is based on finding the median, it should only be used as the measure of spread when the median is the measure of center. You shouldn't mix and match saying the mean is the measure of center and then reporting IQR as the measure of spread.
Thank you and good luck!
Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS
The difference between the third and first quartiles. It represents the range in which the middle 50% of the data points lie.
The difference between the largest and smallest number in a data set.