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

Explanation:

Step1: Identify median in box - and - whisker plot

The line inside the box represents the median. For City A, the median is around 65°F, and for City B, the median is around 70°F. So City B has a larger median.

Step2: Identify highest value in box - and - whisker plot

The end of the right - hand whisker represents the highest value. City A's highest value is around 80°F and City B's highest value is around 90°F. So City B has the highest noon temperature.

Step3: Calculate range

The range is the difference between the highest and lowest values. For City A, the lowest value is around 60°F and the highest is around 80°F, so the range is \(80 - 60=20\)°F. For City B, the lowest value is around 55°F and the highest is around 90°F, so the range is \(90 - 55 = 35\)°F. So City A has a smaller range.

Step4: Calculate inter - quartile range (IQR)

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1), represented by the ends of the box. For City A, Q1 is around 62°F and Q3 is around 70°F, so \(IQR_A=70 - 62 = 8\)°F. For City B, Q1 is around 65°F and Q3 is around 75°F, so \(IQR_B=75 - 65 = 10\)°F. So City B has a larger IQR.

Answer:

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