Question

use the box - and - whisker plot to answer the questions below.
(a) which of these best describes the weights (in kilograms) of the pumpkins in the sample?
○ there were more pumpkins with a weight under 27 than with a weight over 27.
○ there were more pumpkins with a weight over 27 than with a weight under 27.
○ the same number of pumpkins had a weight under 27 as had a weight over 27.
(b) which of the following intervals gives the middle 50% of the data?
○ 27 to 36
○ 27 to 32
○ 32 to 36
○ 15 to 32
(c) 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?)

Explanation:

Step1: Understand the box - and - whisker plot

A box - and - whisker plot shows the minimum, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum values of a data set. The range is calculated as $Range=Max - Min$.

Step2: Find the minimum and maximum values

From the box - and - whisker plot, the minimum value (lightest weight) is \(15\) kg and the maximum value (heaviest weight) is \(36\) kg.

Step3: Calculate the range

Using the formula \(Range = Max - Min\), we substitute \(Max = 36\) and \(Min=15\). So, \(Range=36 - 15=21\). But wait, no, actually, in a box - and - whisker plot, the range is the difference between the maximum and the minimum. Looking at the options for part (c), we should re - check. The minimum is \(15\) and the maximum is \(36\), so \(Range=36 - 15 = 21\). But let's check the options again. Wait, no, for part (c), the formula \(Range=Max - Min\) is correct. The minimum value (the left - most end of the whisker) is \(15\) and the maximum value (the right - most end of the whisker) is \(36\).

Answer:

(a) There were more pumpkins with a weight under 27 than with a weight over 27.
(b) 27 to 36
(c) 15 to 36