To compute the interquartile range (IQR), we need to follow these steps:

1. Order the data (already ordered in your list).
2. Determine the first quartile (Q1): This is the median of the first half of the data.
3. Determine the third quartile (Q3): This is the median of the second half of the data.
4. Compute the IQR: Subtract Q1 from Q3.

Step 1: Locate Q1 and Q3

Given the ordered dataset:

• $Q1$ is the median of the lower half of the data (excluding the overall median).
• $Q3$ is the median of the upper half of the data (excluding the overall median).

Since there are 24 data points, split into:

• Lower half: 12 data points
• Upper half: 12 data points

Step 2: Calculate Q1 and Q3

• Q1: The median of the first 12 data points (32.6 to 38.5). Since there are 12 data points, the median will be the average of the 6th and 7th values:

  • $Q1 = \frac{36.2 + 37.5}{2} = 36.85$

• Q3: The median of the last 12 data points (38.7 to 49.0). The median will be the average of the 6th and 7th values:

  • $Q3 = \frac{41.7 + 42.2}{2} = 41.95$

Step 3: Calculate the IQR

• $IQR = Q3 - Q1$
• $IQR = 41.95 - 36.85 = 5.1$

Final Answer

The interquartile range (IQR) is 5.1 mpg. It is the range of the middle 50% of the data.

Do you want more details or have any questions about this?

Here are five related questions:

1. How do you interpret a high IQR in a dataset?
2. What does a low IQR indicate about the spread of data?
3. How can outliers affect the IQR?
4. What other measures of spread can be used besides IQR?
5. How is the IQR useful in identifying outliers?

Tip: When analyzing data, always check for outliers as they can significantly influence the IQR and other statistical measures.