Question

use the box - and - whisker plot to answer the questions below. (a) which of the following intervals gives the middle 50% of the data? 16 to 23 19 to 23 23 to 31 19 to 31 (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 23 than with a weight over 23. there were more pumpkins with a weight over 23 than with a weight under 23. the same number of pumpkins had a weight under 23 as had a weight over 23.

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 ($Q_3$). From the plot, $Q_1 = 19$ and $Q_3=31$. So the middle 50% of the data is in the interval 19 to 31.

Step2: Calculate the range

The range of a data - set in a box - and - whisker plot is given by the difference between the maximum and minimum values. The minimum value is 10 and the maximum value is 40. So the range is $40 - 10=30$.

Step3: Analyze the median property

The line inside the box is the median. In a box - and - whisker plot, 50% of the data is below the median and 50% is above the median. The median is 23. So the same number of pumpkins had a weight under 23 as had a weight over 23.

Answer:

(a) 19 to 31
(b) 30
(c) The same number of pumpkins had a weight under 23 as had a weight over 23.