Question

esteban recorded his monthly expenses for five months as follows: $215.40, $218.75, $230.50, $260.25, and $223.60. after arranging the expenses in ascending order and calculating the quartiles, what is the inter - quartile range (iqr) of his monthly expenses? $35.00 $11.50 $44.85 $8.20

Explanation:

Step1: Arrange data in ascending order

The data is already in ascending order: $215.40, 218.75, 230.50, 260.25, 223.60$.

Step2: Find the median (Q2)

Since $n = 5$ (odd - numbered data set), the median is the middle - value. So, $Q2=230.50$.

Step3: Find Q1

The lower half of the data is $215.40, 218.75$. The median of the lower half is $Q1=\frac{215.40 + 218.75}{2}=\frac{434.15}{2}=217.075$.

Step4: Find Q3

The upper half of the data is $260.25, 223.60$. The median of the upper half is $Q3=\frac{260.25+223.60}{2}=\frac{483.85}{2}=241.925$.

Step5: Calculate the inter - quartile range (IQR)

$IQR = Q3 - Q1=241.925-217.075 = 24.85$.

Answer:

$24.85$