Question

data analysis and probability
interpreting a box - and - whisker plot: problem type 2
judges at a fishing competition measured the length (in centimeters) of each fish caught during the competition. the box - and - whisker plot
(sometimes called a boxplot) summarizes the data.
use the box - and - whisker plot to answer the questions below.
(a) which of these best describes the lengths (in centimeters) of the fish caught during the competition?
there were more fish with a length under 50 than with a length over 50.
there were more fish with a length over 50 than with a length under 50.
the same number of fish had a length under 50 as had a length over 50.
(b) which of the following intervals gives the middle 50% of the data?
50 to 54 50 to 53 53 to 54 43 to 53

Explanation:

Step1: Understand box - and - whisker plot properties

A box - and - whisker plot divides the data into four equal parts (quartiles). The left half of the box represents the lower \(25\%\) of the data, and the right half represents the upper \(25\%\) of the data. The box itself (from the first quartile \(Q_1\) to the third quartile \(Q_3\)) represents the middle \(50\%\) of the data.

Step2: Analyze part (a)

In a box - and - whisker plot, the length of the whiskers and the box does not represent the number of data points. The box - and - whisker plot divides the data into four equal - sized groups (each group is \(25\%\) of the data). The part of the data under \(50\) (if \(50\) is the median) is \(50\%\) and the part over \(50\) is also \(50\%\).

Step3: Analyze part (b)

The middle \(50\%\) of the data is represented by the box in the box - and - whisker plot. Looking at the plot (assuming the left - hand side of the box is \(43\) and the right - hand side of the box is \(53\))

Answer:

(a) The same number of fish had a length under 50 as had a length over 50.
(b) \(43\) to \(53\)