Question

in the data set below, what is the interquartile range? 2 4 5 6 8

Explanation:

Step1: Arrange data in order

The data set 2, 4, 5, 6, 8 is already in ascending - order.

Step2: Find the median (Q2)

There are 5 data points. The median is the 3rd value. So, Q2 = 5.

Step3: Find Q1

The lower half of the data is 2, 4. The median of the lower half is $\frac{2 + 4}{2}=3$, so Q1 = 3.

Step4: Find Q3

The upper half of the data is 6, 8. The median of the upper half is $\frac{6+8}{2}=7$, so Q3 = 7.

Step5: Calculate the inter - quartile range (IQR)

IQR=Q3 - Q1. Substitute Q1 = 3 and Q3 = 7, we get IQR = 7 - 3 = 4.

Answer:

4