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:

• (a) In a box - and - whisker plot, the end of the right - most whisker (or the outlier point if there is one) represents the maximum value. For City A, the right - most point is at a higher temperature value than that of City B.
• (b) The line inside the box of a box - and - whisker plot represents the median. By comparing the positions of the median lines of City A and City B, we can see which one is larger.
• (c) For a box - and - whisker plot, the part of the data above a certain value can be estimated. If we consider the position of \(78^{\circ}F\) relative to the boxes and whiskers of the two cities. For City B, the right - end of the box (third quartile) is at \(78^{\circ}F\), and half of its data (from the third quartile to the maximum) is above \(78^{\circ}F\). For City A, the third quartile is above \(78^{\circ}F\), but less than half of its data is above \(78^{\circ}F\) (since the box is to the left of where half - above would be for a higher proportion).
• (d) The inter - quartile range (IQR) is calculated as \(Q3 - Q1\) (where \(Q1\) is the first quartile and \(Q3\) is the third quartile). The length of the box in a box - and - whisker plot represents the IQR. By comparing the lengths of the boxes of City A and City B.

Answer:

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