Question: The following data shows the scores of a class: 15, 20, 22, 25, 30, 35, 40, 50. What is the interquartile range (IQR)?
A) 25
B) 20.5
C) 15
D) 16.5
Solution:
First, arrange the data (already sorted).
To find Q1:
Lower half: 15, 20, 22, 25
Q1 = average of 20 and 22 = 21
To find Q3:
Upper half: 30, 35, 40, 50
Q3 = average of 35 and 40 = 37.5
Calculate the IQR:
IQR=Q3−Q1=37.5−21=16.5
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