Question

in the data set below, what is the interquartile range? 53 72 73 73 76 89 90

Explanation:

Step1: Find the median (Q2)

The data set has 7 values. The median is the 4th value. So, \( Q_2 = 73 \).

Step2: Split the data into lower and upper halves

Lower half: \( 53,72,73 \). Upper half: \( 76,89,90 \).

Step3: Find Q1 (median of lower half)

For \( 53,72,73 \), \( Q_1 = 72 \).

Step4: Find Q3 (median of upper half)

For \( 76,89,90 \), \( Q_3 = 89 \).

Step5: Calculate the inter - quartile range (IQR)

\( IQR=Q_3 - Q_1 \). So, \( IQR = 89 - 72 \).

Answer:

\( 17 \)