Question

use the box-and-whisker plot to answer the questions below.

weight of pumpkin (in kilograms)

(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?
15 to 33
27 to 33
33 to 35
27 to 35

(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:

Part (a)

In a box - and - whisker plot, the median divides the data into two equal parts (50% below and 50% above). The lower half (below the median) and the upper half (above the median) can be analyzed. The number of data points below the median (weight under 27) and above the median (weight over 27) should be the same because the median splits the data set into two halves with equal number of observations. So the statement "The same number of pumpkins had a weight under 27 as had a weight over 27" is correct.

The middle 50% of the data in a box - and - whisker plot is represented by the inter - quartile range (IQR), which is the range between the first quartile (\(Q_1\)) and the third quartile (\(Q_3\)). From the box - and - whisker plot, we can see that the box (which represents the middle 50% of the data) is between 27 and 35. So the interval that gives the middle 50% of the data is 27 to 35.

Step 1: Recall the formula for range

The range of a data set is calculated as \(Range=\text{Maximum value}-\text{Minimum value}\)

Step 2: Identify maximum and minimum values

From the box - and - whisker plot, the minimum value (the left - most whisker) is 15 and the maximum value (the right - most whisker) is 50.

Step 3: Calculate the range

\(Range = 50 - 15=35\)

Answer:

The same number of pumpkins had a weight under 27 as had a weight over 27.

Part (b)