Question

What is the interquartile range of the data in the box plot below?

1.5, 12, 14, 29, 45, 48, 61, 72, 84, 96
A. 8
B. 12
C. 23
D. 15

Answer 1

The interquartile range of the given data set is 58.

Step-by-step explanation:

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

1. Arrange the data in numerical order: 1.5, 12, 14, 29, 45, 48, 61, 72, 84, 96
2. Calculate the position of Q1: (n+1)/4 = (10+1)/4 = 2.75, which rounds up to the third value in the data set, 14
3. Calculate the position of Q3: 3(n+1)/4 = 3(10+1)/4 = 8.25, which rounds up to the eighth value in the data set, 72
4. Calculate the interquartile range: IQR = Q3 - Q1 = 72 - 14 = 58

Therefore, the interquartile range of the given data set is 58.