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?) 23 (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 box in a box - and - whisker plot represents the middle 50% of the data. The lower end of the box is the first quartile ($Q_1$) and the upper end is the third quartile ($Q_3$).

Step2: Identify $Q_1$ and $Q_3$ from the plot

From the box - and - whisker plot, assume $Q_1 = 22$ and $Q_3=30$. So the interval for the middle 50% of the data is 22 to 30.

Step3: Calculate the range

The range of a data set is given by $R=\text{Max}-\text{Min}$. From the plot, assume $\text{Max} = 43$ and $\text{Min}=20$. So $R = 43 - 20=23$.

Step4: Analyze the position of the median

The line inside the box is the median. If the median is at 22, half of the data is below 22 and half is above 22.

Answer:

(a) 22 to 30
(b) 23
(c) The same number of pumpkins had a weight under 22 as had a weight over 22.