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 ca
use the box - and - whisker plots to answer the questions.
(a) which city had the highest noon temperature?
(b) which city had a smaller range of noon temperatures?
(c) which city had noon temperatures with a larger interquartile range (iqr)?
(d) which city had a larger median noon temperature?

Explanation:

Step1: Understanding range

The range is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value} \). For box - and - whisker plots, the end of the whisker (or the single point if there are outliers) represents the maximum and minimum. Observing the maximum values: City A has a lower maximum than City B.

Step2: Understanding inter - quartile range (IQR)

The IQR is \( \text{IQR}=Q_{3}-Q_{1} \), where \( Q_{1} \) is the first quartile and \( Q_{3} \) is the third quartile. The length of the box in a box - and - whisker plot represents the IQR. City B's box (IQR) is longer than City A's.

Step3: Understanding median

The median is represented by the line inside the box of the box - and - whisker plot. By comparing the positions of the median lines (the vertical lines inside the boxes) for City A and City B, we can see their relative magnitudes.

Answer:

(a) City B
(b) City A
(c) City B
(d) (Since no content for (d) is fully visible in the image, but following the pattern of using box - and - whisker plot features (e.g., if it was about some other measure like mean (if we assume symmetry and use median as a proxy in symmetric cases) or another quartile - related measure, but with the given info) if it was about a measure where we compare plot features: (If it was about a measure like the position of \( Q_{1}\) or \( Q_{3}\) in a certain context, but with the current visible info, if it was a repetition of a previous logic)