Question

what is the interquartile range of this data set? 2,5,9,11,18,30,42,48,55,73,81
a. 21
b. 46
c. 25
d. 79

Explanation:

Step1: Arrange data in order

The data set is already in ascending order: 2, 5, 9, 11, 18, 30, 42, 48, 55, 73, 81.

Step2: Find the median (Q2)

There are 11 data - points. The median is the 6th value. So, Q2 = 30.

Step3: Find Q1

The lower half of the data is 2, 5, 9, 11, 18. The median of the lower half (Q1) is the 3rd value, so Q1 = 9.

Step4: Find Q3

The upper half of the data is 42, 48, 55, 73, 81. The median of the upper half (Q3) is the 3rd value of this half, so Q3 = 55.

Step5: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1. Substitute Q1 = 9 and Q3 = 55 into the formula: IQR = 55 - 9=46.

Answer:

B. 46