The question you're asking about seems to involve determining whether a value is an outlier based on a data set and using the interquartile range (IQR). The image also includes some handwritten notes for calculations related to outliers.

To answer part (a):

Step 1: Find the Interquartile Range (IQR):

The formula to detect outliers uses the IQR, which is the difference between the third quartile (Q3) and the first quartile (Q1):

$\text{IQR} = Q3 - Q1$

The next step is to calculate the boundaries for outliers using the following formulas:

• Lower Outlier Boundary = $Q1 - 1.5 \times \text{IQR}$
• Upper Outlier Boundary = $Q3 + 1.5 \times \text{IQR}$

If a value is below the lower boundary or above the upper boundary, it's considered an outlier.

To answer part (b):

To prove that a particular number is an outlier, you'd plug the values into the formula and check if the number is beyond the calculated upper or lower boundaries.

From the image, it looks like there’s a partial calculation:

• $4.9 + 1.5(4.9 - 2.1)$ = 4.9 + 4.2 = 9.1$$

This appears to be an upper boundary calculation, and the value beyond this upper boundary would be considered an outlier.

Do you have the dataset for per-capita health spending or want further clarification on specific steps? Let me know if you need help with anything further or an explanation of how to interpret this!