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?

Explanation:

Step1: Arrange data in ascending order

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

Step2: Find the median (Q2)

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

Step3: Split data into lower and upper halves

The lower half is $200, 205, 210, 210, 210, 215$. The upper half is $215, 220, 220, 225, 230$.

Step4: Find Q1 and Q3

For the lower half ($n = 6$), $Q1$ is the average of the 3rd and 4th ordered values. So, $Q1=\frac{210+210}{2}=210$. For the upper half ($n = 6$), $Q3$ is the average of the 3rd and 4th ordered values. So, $Q3=\frac{220 + 220}{2}=220$.

Step5: Calculate the IQR

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

Answer:

$10$