Question

a farmer weighed a sample of pumpkins from her crop. she recorded the weight (in kilograms) of each pumpkin. 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 the following intervals gives the middle 50% of the data? 19 to 30, 19 to 22, 22 to 30, 16 to 22 (b) 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?) (c) which of these best describes the weights (in kilograms) of the pumpkins in the sample? there were more pumpkins with a weight under 22 than with a weight over 22. there were more pumpkins with a weight over 22 than with a weight under 22. the same number of pumpkins had a weight under 22 as had a weight over 22.

Explanation:

Step1: Recall box - and - whisker plot properties

The middle 50% of the data in a box - and - whisker plot is represented by the box. The lower quartile (Q1) is the left - hand side of the box and the upper quartile (Q3) is the right - hand side of the box. Looking at the box - and - whisker plot, the box ranges from 22 to 30.

Step2: Find the range for part (b)

The range of the data is the difference between the maximum and minimum values. The maximum value (end of the right whisker) is 40 and the minimum value (end of the left whisker) is 15. So the range is \(40 - 15=25\).

Step3: Analyze part (c)

The median of the box - and - whisker plot divides the box into two parts. The left part of the box represents the lower 25% of the data within the middle 50% and the right part represents the upper 25% of the data within the middle 50%. Since the box ranges from 22 to 30, more pumpkins have a weight over 22 than under 22.

Answer:

(a) 22 to 30
(b) 25
(c) There were more pumpkins with a weight over 22 than with a weight under 22.