The interquartile range is connected to the range of data. It’s sometimes called the fourth spread.
Here is a short reminder about range:
Theory
The range tells us the difference between the highest and lowest values in a data set:
Theory
The interquartile range tells us the difference between the first quartile, , and third quartile, , of the data:
How do you find and ? You find them like this:
Rule
Theory
The semi-interquartile range measures half of the interquartile range:
Example 1
The age of a group of young gymnasts are 4, 5, 6, 3, 6, 12, 12, 14, 15, 13, 12, 12, 13, 14 and 15. Find the range, the interquartile range, and the semi-interquartile range.
First you arrange the data in ascending order:
You find the range from the formula above:
The range is 12 years.
This is how you find the interquartile range:
The interquartile range is 8 years.
Put into the formula of semi-interquartile range and calculate:
The semi-interquartile range is 4 years.