Paula compares the high temperatures in City 1 and City 2 for one week. In City​ 1, the range in temperature is 20degreesF and the interquartile range​ (IQR) is 4degreesF. In City​ 2, the range in temperature is 9degreesF and the IQR is 4degreesF. What might you conclude about the weather pattern in each city based on the ranges and interquartile​ ranges?

Question

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Part 1
Choose the correct answer below.
A.
The weather pattern in City 1 is more consistent than the weather pattern in City 2.
B.
The weather pattern in City 2 is more consistent than the weather pattern in City 1.
C.
The weather pattern in City 1 and City 2 are equally consistent.
D.
The range and interquartile range do not provide enough information to make a conclusion.
Choose the correct answer below.

Answer 1

To analyze the weather patterns in City 1 and City 2 based on the range and interquartile range (IQR), we need to consider the following:

• Range: This measures the difference between the highest and lowest temperatures. A larger range indicates greater variability in temperatures.
• Interquartile Range (IQR): This measures the range of the middle 50% of the data. A smaller IQR indicates that the middle portion of the data is more clustered together, suggesting more consistency in the temperatures.

City 1:

• Range: 20°F (indicating a wider spread of temperatures)
• IQR: 4°F (indicating that the temperatures in the middle 50% are relatively close together)

City 2:

• Range: 9°F (indicating less variability than City 1)
• IQR: 4°F (same measure of consistency in the middle 50% of temperatures as City 1)

Conclusion:

City 1 has a much larger range of temperatures compared to City 2, indicating that temperatures fluctuate more widely. However, both cities have the same interquartile range (IQR), which suggests that the middle 50% of temperatures in both cities are comparable in consistency.

Given this information, we can conclude that:

B. The weather pattern in City 2 is more consistent than the weather pattern in City 1.

City 2 has a smaller range of temperatures, which suggests less variability overall, while both cities have the same IQR, indicating similar consistency in the central portion of their temperature distributions.