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 more noon temperatures above 82°f? (b) which city had the highest noon temperature? (c) which city had noon temperatures with a larger interquartile range (iqr)? (d) which city had a larger median noon temperature?

Explanation:

Step1: Understand Box - and - Whisker Plots

A box - and - whisker plot shows the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum values of a data set. The interquartile range (IQR) is $IQR = Q_3 - Q_1$.

Step2: Analyze Part (a)

For temperatures above \(82^{\circ}F\):

• In City A, the third quartile (\(Q_3\)) is around \(80^{\circ}F\). So, less than \(25\%\) of the data (since \(Q_3\) represents the \(75^{th}\) percentile) is above \(80^{\circ}F\).
• In City B, the third quartile (\(Q_3\)) is above \(82^{\circ}F\). So, more than \(25\%\) of the data is above \(82^{\circ}F\).

Step3: Analyze Part (b)

The maximum value (the end of the whisker) for City A is higher than that for City B.

Step4: Analyze Part (c)

• For City A: Estimate \(Q_1\approx72\), \(Q_3\approx80\), \(IQR = 80 - 72=8\).
• For City B: Estimate \(Q_1\approx78\), \(Q_3\approx84\), \(IQR = 84 - 78 = 6\). So City A has a larger IQR.

Step5: Analyze Part (d)

The median (the line inside the box) for City B is higher than that for City A.

Answer:

(a) City B
(b) City A
(c) City A
(d) City B