Question

use the box - and - whisker plot to answer the questions below. (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 25 than with a weight over 25. there were more pumpkins with a weight over 25 than with a weight under 25. the same number of pumpkins had a weight under 25 as had a weight over 25. (c) which of the following intervals gives the lowest 25% of the data? 10 to 14, 14 to 16, 14 to 20, 16 to 20

Explanation:

Step1: Recall range definition

The range of a data - set in a box - and - whisker plot is the difference between the maximum and minimum values.

Step2: Identify max and min from plot

From the box - and - whisker plot, the minimum value is 10 and the maximum value is 50.

Step3: Calculate the range

Range = Maximum value - Minimum value = 50 - 10=40.

For part (b):
In a box - and - whisker plot, the median divides the data into two halves. The lower half of the data is from the minimum value to the median and the upper half is from the median to the maximum value. The box represents the middle 50% of the data. The lower quartile ($Q_1$) is the median of the lower half and the upper quartile ($Q_3$) is the median of the upper half.
If we consider the value 25 on the number line of the box - and - whisker plot, we can see that more pumpkins have a weight under 25 than over 25.

For part (c):
The inter - quartile range (IQR) is $Q_3 - Q_1$ and represents the middle 50% of the data. The lower 25% of the data is from the minimum value to $Q_1$. Looking at the box - and - whisker plot, we need to find the interval that contains the lowest 25% of the data. The lowest 25% of the data is from the minimum value (10) to the lower quartile. From the plot, we can see that the interval 10 to 14 contains the lowest 25% of the data.

Answer:

(a) 40
(b) There were more pumpkins with a weight under 25 than with a weight over 25.
(c) 10 to 14