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? (b) which city had the highest noon temperature? (c) which city had noon temperatures with a larger interquartile range (iqr)? (d) which city had more noon temperatures above 78 °f?

Explanation:

Step1: Locate medians

The vertical line inside the box of a box - and - whisker plot represents the median. For City A, the median is around 75°F. For City B, the median is around 70°F. So City A has a larger median.

Step2: Locate maximum values

The end - point of the right - hand whisker (or the outlier point if present) represents the maximum value. For City A, the maximum is around 85°F. For City B, the maximum is around 95°F. So City B has the highest noon temperature.

Step3: Calculate IQR

The inter - quartile range (IQR) is the length of the box, which is Q3 - Q1. For City A, Q1 is around 65°F and Q3 is around 80°F, so IQR = 80 - 65=15°F. For City B, Q1 is around 65°F and Q3 is around 75°F, so IQR = 75 - 65 = 10°F. So City A has a larger IQR.

Step4: Analyze values above 78°F

For City A, the right - hand part of the box (from Q3) and the right - hand whisker represent values above Q3 (around 80°F). For City B, part of the box (from 78°F to Q3 around 75°F) and the right - hand whisker represent values above 78°F. By visual inspection, City B has more noon temperatures above 78°F.

Answer:

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