In the data set below, what is the interquartile range?
12 16 19 27 34 43 49 52 53 71 75 87
To find the interquartile range, we first need to find the first quartile (Q1) and third quartile (Q3).
The total number of data points is 12, so the median will be the average of the 6th and 7th numbers when the data set is ordered.
Median = (34 + 43) / 2 = 38.5
For the lower half of the data set (12, 16, 19, 27, 34, 38.5), the median is the average of the 3rd and 4th numbers when the half is ordered.
Q1 = (16 + 19) / 2 = 17.5
For the upper half of the data set (38.5, 43, 49, 52, 53, 71, 75, 87), the median is the average of the 4th and 5th numbers when the half is ordered.
Q3 = (52 + 53) / 2 = 52.5
Interquartile Range (IQR) = Q3 - Q1 = 52.5 - 17.5 = 35.
Therefore, the interquartile range is 35.