A measure of spread
Now we can define a new measure of spread based entirely on the lower and upper quartiles.
The interquartile range
The interquartile range (sometimes abbreviated to IQR) is the distance between the lower and upper quartiles:
Note that this value is independent of the sizes of and .
Example 16 The prices of small televisions, yet again!
For the batch of 20 television prices in Example 14 (Subsection 3.2),
So the interquartile range is £50.
Activity 11 Coffee prices again
Calculate both the range and the interquartile range of the batch of 15 coffee prices, last seen in Figure 17 (Subsection 3.2).
The range is the distance between the extremes:
The interquartile range is the distance between the quartiles:
You may be wondering why you are being asked to learn a new measure of spread when you already know the range. As a measure of spread, the range is not very satisfactory because it is not resistant to the effects of unrepresentative extreme values. (Resistant measures were explained in Subsection 1.4.) The interquartile range, by contrast, is a highly resistant measure of spread (because it is not sensitive to the effects of values lying outside the middle 50% of the batch) and it is generally the preferred choice.
Example 17 Comparing the resistance of the range and the IQR
Suppose the price of the most expensive jar of coffee is reduced from 369p to 325p. How does this affect the range and the interquartile range of the batch of coffee prices in Figure 17 (Subsection 3.2)?
The new range is
a lot less than the original value of 101p (found in Activity 11). The interquartile range is unchanged.