Question

calculating measures of spread related to expenses
esteban recorded his monthly expenses for five months as follows: $215.40, $248.75, $230.50, $260.25, and $223.60. after arranging the expenses in ascending order and calculating the quartiles, what is the interquartile range (iqr) of his monthly expenses?
$35.00
$8.20
$11.50
$44.85

Explanation:

Step1: Arrange data in ascending order

$215.40, 223.60, 230.50, 248.75, 260.25$

Step2: Find the median (Q2)

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

Step3: Find Q1

The lower half of the data is $215.40, 223.60$. The median of the lower half is $Q1=\frac{215.40 + 223.60}{2}=219.50$.

Step4: Find Q3

The upper half of the data is $248.75, 260.25$. The median of the upper half is $Q3=\frac{248.75+260.25}{2}=254.50$.

Step5: Calculate the IQR

$IQR = Q3 - Q1=254.50 - 219.50 = 35.00$

Answer:

$35.00$