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 noon temperatures with a larger interquartile range (iqr)? (b) which city had more noon temperatures above 75°f?

Explanation:

Step1: Recall IQR formula

IQR = Q3 - Q1, where Q3 is the third - quartile and Q1 is the first - quartile. For City A, assume Q1 is around 72 and Q3 is around 80, so IQR_A=80 - 72 = 8. For City B, assume Q1 is around 65 and Q3 is around 75, so IQR_B=75 - 65 = 10.

Step2: Compare IQRs

Since 10>8, City B has a larger IQR.

Step3: Analyze temperatures above 75°F

In a box - and - whisker plot, the right part of the box and the right whisker represent values above Q2 (the median). For City A, the median is around 75°F, so about 50% of the data is above 75°F. For City B, the median is below 75°F, so more than 50% of the data is above 75°F.

Answer:

(a) City B
(b) City B