Question

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) what is the difference of the longest length and the shortest length of fish caught during the competition? (that is, what is the range of the data?) (b) 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. (c) which of the following intervals gives the lowest 25% of the data? 30 to 42 42 to 45 42 to 46 45 to 46

Explanation:

Part (a)

Step1: Recall the formula for range

The range is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value} \).

Step2: Identify maximum and minimum values from the box - plot

From the box - plot, the maximum value \( M = 62 \) and the minimum value \( m=41 \).

Step3: Calculate the range

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Part (b)

Step1: Recall the property of the box - plot

In a box - plot, the left whisker and the left part of the box represent the lower \( 50\%\) of the data, and the right whisker and the right part of the box represent the upper \( 50\%\) of the data.

Step2: Analyze the position of the median (the line inside the box)

The median of the box - plot is closer to the lower half. So, there were more fish with a length under \( 50 \) than with a length over \( 50 \).

Part (c)

Step1: Recall the property of the lower quartile (\(Q_1\))

The lower \( 25\%\) of the data is below \(Q_1\).

Step2: Identify the interval for the lower \(25\%\)

From the box - plot, the lower \(25\%\) of the data lies in the interval \(42\) to \(46\).

Answer:

(a) The range of the data is \(21\).
(b) There were more fish with a length under \(50\) than with a length over \(50\).
(c) The interval \(42\) to \(46\) gives the lowest \(25\%\) of the data.