Question

your answer is incorrect.

• (a): your answer is incorrect.
• (d): your answer is incorrect.

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 a larger median noon temperature?
(b) which city had a smaller range of noon temperatures?
(c) which city had noon temperatures with a larger interquartile range (iqr)?
(d) which city had the highest noon temperature?

Explanation:

Step1: Recall box - and - whisker plot properties

In a box - and - whisker plot, the line inside the box represents the median. The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). The inter - quartile range (IQR) is \( \text{IQR}=Q_3 - Q_1 \) (where \( Q_1 \) is the first quartile and \( Q_3 \) is the third quartile). The end of the right - most whisker (or the outlier point) represents the maximum value.

Step2: Analyze the median

For City A, the median (the line inside the box) is at a lower value on the number line compared to City B. So City B has a larger median.

Step3: Analyze the range

For City A: Let's assume the minimum is \( x_{A,\text{min}} \) and the maximum is \( x_{A,\text{max}} \). For City B: Let's assume the minimum is \( x_{B,\text{min}} \) and the maximum is \( x_{B,\text{max}} \). By looking at the whiskers, the distance between the maximum and minimum for City A (\( x_{A,\text{max}}-x_{A,\text{min}} \)) is smaller than for City B (\( x_{B,\text{max}}-x_{B,\text{min}} \)). So City A has a smaller range.

Step4: Analyze the IQR

The length of the box (which represents the IQR) for City B is larger than for City A. So City B has a larger IQR.

Step5: Analyze the maximum value

By looking at the right - most points (the end of the whiskers or outlier points), City B has the highest noon temperature.

Answer:

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