In the data set below, what is the interquartile range?
53 53 74 88 98
To find the interquartile range, first we need to find the first quartile (Q1) and third quartile (Q3).
The data set given is: 53, 53, 74, 88, 98
Arranging the data in ascending order: 53, 53, 74, 88, 98
Q1 is the median of the lower half of the data, which is the median of {53, 53} = 53
Q3 is the median of the upper half of the data, which is the median of {74, 88, 98} = 88
Interquartile range (IQR) = Q3 - Q1
IQR = 88 - 53
IQR = 35
Therefore, the interquartile range of the given data set is 35.