Question

(a) what is the difference of the heaviest weight and the lightest weight of pumpkins in the sample? (that is, what is the range of the data?)(b) which of these best describes the weights (in kilograms) of the pumpkins in the sample?there were more pumpkins with a weight under 21 than with a weight over 21.there were more pumpkins with a weight over 21 than with a weight under 21.the same number of pumpkins had a weight under 21 as had a weight over 21.(c) which of the following intervals gives the highest 25% of the data?21 to 3232 to 3821 to 3838 to 50

Explanation:

Step1: Find the range

The range is calculated as the maximum value minus the minimum value. From the box - and - whisker plot, the minimum value is \(14\) and the maximum value is \(40\).

$$ \text{Range}=40 - 14=26 $$

Step2: Analyze part (b)

The median of the box - and - whisker plot divides the data into two halves. The left part of the box (lower half) and the right part (upper half). The value \(21\) is the lower quartile (\(Q_1\)). The number of data points below \(Q_1\) (weight under \(21\)) is \(25\%\) of the data, and the number of data points above \(Q_3\) (weight over \(32\)) is \(25\%\) of the data. So, there were more pumpkins with a weight over \(21\) than with a weight under \(21\).

Step3: Analyze part (c)

The highest \(25\%\) of the data is from the upper quartile (\(Q_3 = 32\)) to the maximum value (\(40\)).

Answer:

(a) The range of the data is \(26\).
(b) There were more pumpkins with a weight over \(21\) than with a weight under \(21\).
(c) \(32\) to \(40\) (assuming a typo in the options, if we consider the correct range for the upper \(25\%\) based on \(Q_3 = 32\) and max \(=40\))