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

Explanation:

Step1: Analyze highest temperature

In a box - and - whisker plot, the end of the rightmost whisker (or the outlier point) represents the maximum value. For City A, the rightmost point (excluding the outlier) is at a higher temperature value on the scale compared to City B.

Step2: Analyze median

The line inside the box represents the median. The median line of City A is at a higher temperature value than that of City B.

Step3: Analyze temperatures above \(78^{\circ}F\)

In a box - and - whisker plot, the box is divided into quartiles. For temperatures above \(78^{\circ}F\), we consider the part of the data to the right of \(78^{\circ}F\). By visual inspection of the plots, City B has a larger portion (in terms of the length of the box and whisker) to the right of \(78^{\circ}F\)

Step4: Analyze IQR

The inter - quartile range (IQR) is the length of the box ( \(Q3 - Q1\) ). By measuring (or visual comparison) the length of the box for each city, City A's box has a greater length.

Answer:

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