Challenge The following box plots show monthly average high temperature from January to December in degrees Fahrenheit for two U.S. cities. Which city should you live in if you want the most variability in​ temperature?

Question

City X
10
15
20
25
30
35
40
45
50
55
60
Degrees Fahrenheit

A box plot titled City X has a number line labeled Degrees Fahrenheit from 10 to 60. A box extends from 30 to 50, with a vertical line segment through the box at 37.5. A horizontal line segment extends from 15 to 30. A horizontal line segment extends from 50 to 60.
City Y
10
15
20
25
30
35
40
45
50
55
60
Degrees Fahrenheit

A box plot titled City Y has a number line labeled Degrees Fahrenheit from 10 to 60. A box extends from 20 to 50, with a vertical line segment through the box at 37.5. A horizontal line segment extends from 10 to 20. A horizontal line segment extends from 50 to 60.
Question content area bottom
Part 1
Which city should you live in if you want the most variability in​ temperature?
A.City Upper X
City Upper X
B.City Upper Y
City Upper Y
C.City Upper X and City Upper Y comma because they have the same variability in temperature.
City Upper X and City Upper Y comma because they have the same variability in temperature.
Which city should you live in if you want the most variability in temperature?

Answer 1

To determine which city has the most variability in temperature based on the box plots provided, we need to look at the range (the difference between the minimum and maximum values) and the interquartile range (IQR), which is the range of the middle 50% of the data (the distance between the first quartile and the third quartile).

For City X:

• Minimum: 15
• Maximum: 60
• IQR (from 30 to 50): \(50 - 30 = 20\)

For City Y:

• Minimum: 10
• Maximum: 60
• IQR (from 20 to 50): \(50 - 20 = 30\)

Observations:

1. The range for City X is \(60 - 15 = 45\).
2. The range for City Y is \(60 - 10 = 50\).
3. For the IQR, City X is 20, and City Y is 30.

Conclusion:

City Y has both a wider range and a larger IQR compared to City X. Therefore, City Y has more variability in temperature.

You should choose B. City Y if you want the most variability in temperature.