Question

hugo’s health expenses for the year were: $200, $210, $220, $215, $210, $225, $215, $205, $220, $210, $215, $230. what is the iqr of his health expenses? options (in boxes): $15, $5, $10, $20

Explanation:

Step1: Order the data

First, we order the health expenses data: $200, $205, $210, $210, $210, $215, $215, $215, $220, $220, $225, $230.

Step2: Find the median (Q2)

The number of data points \( n = 12 \), which is even. The median is the average of the 6th and 7th values. The 6th value is \( 215 \) and the 7th value is \( 215 \), so \( \text{Median} = \frac{215 + 215}{2} = 215 \).

Step3: Find Q1 (median of lower half)

The lower half of the data (values below the median) is: $200, $205, $210, $210, $210, $215. The number of values here is \( 6 \) (even). The median of the lower half (Q1) is the average of the 3rd and 4th values. The 3rd value is \( 210 \) and the 4th value is \( 210 \), so \( Q1 = \frac{210 + 210}{2} = 210 \).

Step4: Find Q3 (median of upper half)

The upper half of the data (values above the median) is: $215, $215, $220, $220, $225, $230. The number of values here is \( 6 \) (even). The median of the upper half (Q3) is the average of the 3rd and 4th values. The 3rd value is \( 220 \) and the 4th value is \( 220 \), so \( Q3 = \frac{220 + 220}{2} = 220 \).

Step5: Calculate IQR

The Inter - Quartile Range (IQR) is calculated as \( IQR=Q3 - Q1 \). Substituting the values of \( Q3 = 220 \) and \( Q1 = 210 \), we get \( IQR = 220-210=10 \).

Answer:

\$10