Finding the Interquartile Range

The interquartile range (IQR) of a data set is found by first identifying the three quartiles and then calculating the difference between the third and the first quartile. Consider the following data set. 1, 3, 4, 4, 5, 6, 6, 8, 8, 10, 10, 11 The interquartile range of the data set can be found by following these four steps.

1

Identify the Median

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First, identify the median of the given data set. Since the number of values is even, the median is the mean of the two middle values.

The median of the data is 6.

2

Identify the Lower and the Upper Half of the Data Set

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The median divides the data into two halves, a lower half and an upper half. For this data, the lower half includes the first six values and the upper half includes the following six.

When there is an odd number of values in the data set, the middle value is excluded from both the lower and upper sets.

3

Find the First and the Third Quartile

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Find the first and the third quartile. The first quartile, Q_1, is the median of the lower set, while the third, Q_3, is the median of the upper set. Here, both quartiles are found the same way the median was found.