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 a smaller range of noon temperatures?

Explanation:

Step1: Recall the definition of range in box - and - whisker plot

The range is calculated as \(Range=Maximum - Minimum\). The maximum value is the end of the right - most whisker.

Step2: Compare the maximum values for City A and City B

Looking at the box - and - whisker plots:

• For City A, the maximum value (end of the right - most whisker) is less than 90.
• For City B, the maximum value (end of the right - most whisker) is 95. So, City B has the highest noon temperature.

Step3: Calculate the range for City A and City B

• For City A:
• Let the minimum value (end of the left - most whisker) be \(x_A\approx70\) and the maximum value (end of the right - most whisker) be \(y_A\approx85\). Then \(Range_A=y_A - x_A\approx85 - 70 = 15\).
• For City B:
• Let the minimum value (end of the left - most whisker) be \(x_B\approx68\) and the maximum value (end of the right - most whisker) be \(y_B = 95\). Then \(Range_B=y_B - x_B=95 - 68=27\).

Answer:

(a) City B
(b) City A