Question

hugos 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? $20 $5 $15 $10

Explanation:

Step1: Sort the data

$200, 205, 210, 210, 210, 215, 215, 215, 220, 220, 225, 230$

Step2: Find the median (Q2)

Since there are 12 data - points, the median is the average of the 6th and 7th ordered values. So, $Q2=\frac{215 + 215}{2}=215$.

Step3: Find the lower half and Q1

The lower half of the data is $200, 205, 210, 210, 210, 215$. The median of the lower half (Q1) is the average of the 3rd and 4th ordered values in the lower - half. So, $Q1=\frac{210+210}{2}=210$.

Step4: Find the upper half and Q3

The upper half of the data is $215, 220, 220, 225, 230$. The median of the upper half (Q3) is the average of the 3rd and 4th ordered values in the upper - half. So, $Q3=\frac{220 + 220}{2}=220$.

Step5: Calculate the IQR

$IQR = Q3 - Q1=220 - 210 = 10$.

Answer:

$10$