Question
The box plots below show the average gas mileage, in miles per gallon, of the cars sold at a dealership in June and in December.
Gas Mileage of Cars Sold in June
2 box plots. The number line goes from 14 to 34. For cars sold in June, the whiskers range from 21 to 33, and the box ranges from 22 to 29. A line divides the box at 24. For Cars sold in December, the whiskers range from 14 to 26, and the box ranges from 18 to 21. A line divides the box at 19.
Gas Mileage of Cars Sold in December
The manager used the table below to compare the measures of center and the measures of variability.
Median
Range
Interquartile Range
Sold in June
24
33 minus 21 = 12
29 minus 22 = 7
Sold in December
19
26 minus 14 = 12
21 minus 16 = 5
What error did the manager make in the table?
The median for June should be 22.
The median for December should be 14.
The interquartile range for December should be 21 minus 18 = 3.
The interquartile range for December should be 26 minus 18 = 8.
Gas Mileage of Cars Sold in June
2 box plots. The number line goes from 14 to 34. For cars sold in June, the whiskers range from 21 to 33, and the box ranges from 22 to 29. A line divides the box at 24. For Cars sold in December, the whiskers range from 14 to 26, and the box ranges from 18 to 21. A line divides the box at 19.
Gas Mileage of Cars Sold in December
The manager used the table below to compare the measures of center and the measures of variability.
Median
Range
Interquartile Range
Sold in June
24
33 minus 21 = 12
29 minus 22 = 7
Sold in December
19
26 minus 14 = 12
21 minus 16 = 5
What error did the manager make in the table?
The median for June should be 22.
The median for December should be 14.
The interquartile range for December should be 21 minus 18 = 3.
The interquartile range for December should be 26 minus 18 = 8.
Answers
GPT-4o mini
Let's evaluate the values from the box plots and the computations made in the table.
1. **Median**:
- For June: The median is correctly identified as 24.
- For December: The median is correctly identified as 19.
2. **Range**:
- For June: The range is calculated as 33 - 21 = 12, which is correct.
- For December: The range is calculated as 26 - 14 = 12, which is also correct.
3. **Interquartile Range (IQR)**:
- For June: The IQR is calculated correctly as 29 - 22 = 7.
- For December: The IQR is stated as 21 - 18 = 5; this is incorrect. The calculation of the IQR should be based on the values at the first and third quartiles (the edges of the box), which are 18 and 21, respectively. The correct calculation is 21 - 18 = 3.
Given the above evaluations, the error made by the manager in the table is:
**The interquartile range for December should be 21 minus 18 = 3.**
1. **Median**:
- For June: The median is correctly identified as 24.
- For December: The median is correctly identified as 19.
2. **Range**:
- For June: The range is calculated as 33 - 21 = 12, which is correct.
- For December: The range is calculated as 26 - 14 = 12, which is also correct.
3. **Interquartile Range (IQR)**:
- For June: The IQR is calculated correctly as 29 - 22 = 7.
- For December: The IQR is stated as 21 - 18 = 5; this is incorrect. The calculation of the IQR should be based on the values at the first and third quartiles (the edges of the box), which are 18 and 21, respectively. The correct calculation is 21 - 18 = 3.
Given the above evaluations, the error made by the manager in the table is:
**The interquartile range for December should be 21 minus 18 = 3.**