Question

cheo paid monthly rents of $800, $820, $825, $810, and $825 over the last five years. what is the interquartile range (iqr) of her rents?

Explanation:

Step1: Order the data

First, we order the rent values: \( \$800, \$810, \$820, \$825, \$825 \)

Step2: Find Q1 (25th percentile)

For a set with \( n = 5 \) data points, the position of Q1 is \( \frac{n + 1}{4}=\frac{5 + 1}{4}=1.5 \). So we take the average of the 1st and 2nd values: \( \frac{800 + 810}{2}=\frac{1610}{2}=805 \)

Step3: Find Q3 (75th percentile)

The position of Q3 is \( \frac{3(n + 1)}{4}=\frac{3(5 + 1)}{4}=4.5 \). We take the average of the 4th and 5th values: \( \frac{825 + 825}{2}=\frac{1650}{2}=825 \)

Step4: Calculate IQR

IQR is \( Q3 - Q1 \), so \( 825 - 805 = 20 \)

Answer:

\( \$20 \)