Question

in the data set below, what is the interquartile range? 17 25 27 39 55 66 66 88 95

Explanation:

Step1: Find the median (Q2)

The data set has 9 values. The median is the 5th value. So, \( Q_2 = 55 \).

Step2: Find Q1 (median of the lower half)

The lower half is \( 17,25,27,39 \). The median of this set (average of 2nd and 3rd values) is \( \frac{25 + 27}{2}=26 \). So, \( Q_1 = 26 \).

Step3: Find Q3 (median of the upper half)

The upper half is \( 66,66,88,95 \). The median of this set (average of 2nd and 3rd values) is \( \frac{66+88}{2} = 77 \). So, \( Q_3=77 \).

Step4: Calculate the inter - quartile range (IQR)

The formula for IQR is \( IQR=Q_3 - Q_1 \). Substitute \( Q_1 = 26 \) and \( Q_3 = 77 \). So, \( IQR=77 - 26=51 \).

Answer:

51