Question

in the data set below, what is the interquartile range? 30 44 58 67 87

Explanation:

Step1: Arrange data in order

30, 44, 58, 67, 87

Step2: Find median (Q2)

Since there are 5 data - points, the median is the 3rd value. So Q2 = 58.

Step3: Find lower half

The lower half is 30, 44. The median of the lower half (Q1) is $\frac{30 + 44}{2}=37$.

Step4: Find upper half

The upper half is 67, 87. The median of the upper half (Q3) is $\frac{67+87}{2}=77$.

Step5: Calculate inter - quartile range

IQR = Q3 - Q1 = 77 - 37 = 33.

Answer:

33