What is the interquartile range of this data set?

2, 5, 9, 11, 18, 30, 42, 55, 58, 73, 81

49

Explanation:

Interquartile range is the difference between the third and the first quartile of a data set.

It is designated by IQR = Q₃ - Q₁.

Then, you must determine first quartile, Q₁, and third quartile, Q₃.

To determine the quartiles you must order the numbers in the data set. They already are ordered.

Then, separate them in two equal parts. When the amount of data in the set is odd, the middle number is the median and it separates the data set into two equal parts:

[ 2, 5, 9, 11, 18 ] 30 [ 42, 55, 58, 73, 81 ]

↑

median

The first quartile, Q₁, is the median of the first half of data. This is the median of [ 2, 5, 9, 11, 18 ]. The median is the value of the middle so it is 9.

Q₁ = 9

The third quartile, Q₃, is the median of the second half of data. This is the median of [ 42, 55, 58, 73, 81 ]. The median, again, is the middle, so it is 58.

Q₃ = 58.

And, IQR = Q₃ - Q₁ = 58 - 9 = 49.