Question

The noon temperatures (in Fahrenheit) for two cities were recorded over a given month.The box-and-whisker plots below (sometimes called boxplots) summarize the noon temperatures for each city. Use the box-and-whisker plots to answer the questions. (a)Which city had the highest noon temperature?(b)Which city had noon temperatures with a larger interquartile range (IQR)?(c)Which city had a smaller range of noon temperatures?(d)Which city had a larger median noon temperature?

Answer 1

Using the given box plot, we can deduce the following:

• City A:

Minimum = 70

Lower quartile, Q1 = 72

Median = 76

Upper quartile, Q3 = 90

Maximum = 82

• City B:

Minimum = 62

Lower quartile, Q1 = 65

Median = 70

Upper quartile, Q3 = 79

Maximum = 85

Let's answer the following question:

• (a) Which city had the highest noon temperature?

The city with the highest temperature will be the city with the greater maximum.

Therefore, the city that had the highest noon temperature is City B.

• (b). Which city had noon temperatures with a larger interquartile range (IQR)?

To find the IQR, apply the formula:

IQR = Q3 - Q1

Thus, we have:

IQR for city A = Q3 - Q1 = 90 - 72 = 18

IQR for city B = Q3 - Q1 = 79 - 65 = 14

Therefore, the city that had noon temperatures with a larger Interquartile range is city A.

• (c). Which city had a smaller range of noon temperatures?

To find the range of each city, apply the formula:

Range = Maximum - Mininmum

Thus, we have the following:

Range of city A = Maximum - Minimum = 82 - 70 = 12

Range of city B = Maximum - Minimum = 85 - 62 = 23

The city with a smaller range of noon temperatures is City A.

• (d). Which city had a larger median noon temperature?

The city with a larger median is City A.

ANSWER:

• (a). City B

,

• (b). City A

,

• (c). City A

,

• (d). City A.