Question content area top
Part 1
Given the five boundary values of a data set, find the interquartile range (IQR).
Minimum
equals
24
First quartile
equals
62
Median
equals
75
Third quartile
equals
115
Maximum
equals
215
To find the interquartile range (IQR), you first need to find the first quartile (Q1) and the third quartile (Q3). Q1 and Q3 divide the data set into four equal parts.
Q1 is the median of the lower half of the data, which in this case is 62.
Q3 is the median of the upper half of the data, which in this case is 115.
Therefore, Q1 = 62 and Q3 = 115.
Now, to find the IQR, subtract Q1 from Q3:
IQR = Q3 - Q1
IQR = 115 - 62
IQR = 53
Therefore, the interquartile range (IQR) of the data set is 53.