The Range of a Set of Numbers

By John Pezzullo

The range of a set of values in your data is the difference between the smallest value (the minimum value) and the largest value (the maximum value):

Range = maximum value – minimum value

So for the IQ example in the preceding section (84, 84, 89, 91, 110, 114, and 116), the minimum value is 84, the maximum value is 116, and the range is 32 (equal to 116 – 84).

The range is extremely sensitive to outliers. If the largest IQ were 150 instead of 116, the range would increase from 32 to 66 (equal to 150 – 84).

Outside of its formal definition in statistics as a single number representing the difference between the minimum and maximum values, the term range can also refer to the two numbers themselves —the minimum and the maximum. For example, suppose that a clinical trial protocol specifies that you’re to enroll only subjects having glucose values within 150 to 250 milligrams per deciliter. People often express this as “within the range” of 150 to 250 milligrams per deciliter (mg/dL).

You may ask whether a subject with a value of exactly 250 falls “within” that range. This possible ambiguity is usually avoided by using the term inclusive or exclusive to specify whether a person who is exactly at the limit of a range is considered within it or not. Some ranges can be inclusive at one end and exclusive at the other end.

You might see the following mathematical shorthand describing a range: 50 < Gluc < 250, which indicates that glucose values are greater than 50 and less than 250 mg/dL. This would be a range with exclusive endpoints. A glucose range with inclusive endpoints could be indicated as 50 ≤ Gluc ≤ 250, indicating that glucose values exactly equal to 50 or 250 would be considered within the range. And an expression like 50 ≤ Gluc < 250 would indicate that a glucose value of exactly 50 is included in the range, but a value of exactly 250 is not.