What is the interquartile range of 54 and 65 and 66 and 68 and 73 and 75 and 75 and 78 and 82 and 82 and 87 and 97?

Answer 1

Since the set of data is arranged in numerical order, first we need to find the median (also called the second quartile), which separates the data into two equal groups, in our case there are 6 numbers in each group.

54 65 66 68 73 75 | 75 78 82 82 87 97

The first quartile (also called the lower quartile) is the middle value of numbers that are below the median, in our case is 67.

54 65 66 | 68 73 75 | 75 78 82 82 87 97

The third quartile (also called the upper quartile) is the middle value of numbers that are above the median, in our case is 82.

54 65 66 | 68 73 75 | 75 78 82 | 82 87 97

The interquartile range is the difference between the first and third quartiles, which is 15, (82 - 67).