in the data set below, what is the interquartile range? 1 2 2 2 4 5 7 7

Answer

Explanation:

Step1: Arrange data in order

The data is already in ascending - order: 1, 2, 2, 2, 4, 5, 7, 7.

Step2: Find the median (Q2)

There are (n = 8) data points. The median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th values. (\frac{n}{2}=4) and (\frac{n}{2}+1 = 5). So, (Q2=\frac{2 + 4}{2}=3).

Step3: Find Q1

The lower - half of the data is 1, 2, 2, 2. There are (n_1 = 4) data points. The median of the lower - half is (Q1=\frac{2+2}{2}=2).

Step4: Find Q3

The upper - half of the data is 4, 5, 7, 7. There are (n_2 = 4) data points. The median of the upper - half is (Q3=\frac{5 + 7}{2}=6).

Step5: Calculate the inter - quartile range (IQR)

(IQR=Q3 - Q1). Substitute (Q1 = 2) and (Q3 = 6) into the formula: (IQR=6 - 2=4).