Essential Statistics

Chapter 3: Measures of Variability

103

3-3 The Interquartile Range

A measure of spread that is not influenced by any extreme values (outliers)

in the data set but still preserves the idea of a range is the

interquartile

range.

Definition: Interquartile Range

The interquartile range is a statistic which measures the spread of the middle

50% of an ordered data set.

The interquartile range is usually denoted by

There are several procedures which one can use to determine the

interquartile range for a set of values. One of these procedures used in

finding the interquartile range is described next.

Procedure for Finding the Interquartile Range

Step 1:

Order the data set from the minimum value to the maximum value.

Step 2:

Find the median of the ordered set. Denote this by

. This value

is called the second quartile for the data set.

Step 3:

Find the median of the first 50 percent of the data set.

The median in

Step 2

not

included for this portion of the

data set. Let this value be denoted by

. This value is called the

first quartile for the data set.

Step 4:

Find the median of the second 50 percent of the data set.

The median in

Step 2

not

included for this portion of the

data set. Let this value be denoted by

. This value is called the

third quartile for the data set.

Step 5:

Compute the interquartile range from the following relationship.