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

Explanation:

(a) Range

• Range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \).
• For City A: assume maximum is \( 85 \) and minimum is \( 60 \), range \(=85 - 60=25 \).
• For City B: assume maximum is \( 80 \) and minimum is \( 60 \), range \(=80 - 60 = 20 \). So City B has a smaller range.

(b) Inter - quartile range (IQR)

• \( \text{IQR}=Q_{3}-Q_{1} \).
• For City A: assume \( Q_{3}=80 \), \( Q_{1}=65 \), \( \text{IQR}=80 - 65=15 \).
• For City B: assume \( Q_{3}=75 \), \( Q_{1}=65 \), \( \text{IQR}=75 - 65 = 10 \). So City A has a larger IQR.

(c) Highest temperature

• By looking at the maximum values (end of the whisker or the outlier point). City A has a higher maximum (assume \( 85 \) for City A and \( 80 \) for City B). So City A has the highest noon temperature.

(d) Median

• The line inside the box is the median. City A's median (assume \( 75 \)) is higher than City B's median (assume \( 70 \)). So City A has a larger median.

Answer:

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