Question

in the data set below, what is the interquartile range? 1 2 2 2 4 4 6 7

Explanation:

Step1: Arrange data in order

1, 2, 2, 2, 4, 4, 6, 7

Step2: Find median (Q2)

Since there are 8 data - points, the median is the average of the 4th and 5th values. $\frac{2 + 4}{2}=3$.

Step3: Find lower half

The lower half is 1, 2, 2, 2. The median of the lower half (Q1) is 2.

Step4: Find upper half

The upper half is 4, 4, 6, 7. The median of the upper half (Q3) is $\frac{4+6}{2}=5$.

Step5: Calculate inter - quartile range

$IQR = Q3 - Q1=5 - 2 = 3$.

Answer:

3