Question

which statement is true about the ranges for the box plots?
number of sales in the morning and the afternoon
morning
afternoon
0 2 4 6 8 10 12 14 16
the range of the morning box plot is the same as the range of the afternoon box plot
the range of the morning box plot is 1 less than the range of the afternoon box plot
the range of the morning box plot is 1 more than the range of the afternoon box plot
the range of the morning box plot is 2 less than the range of the afternoon box plot

Explanation:

Step1: Recall the formula for range

The range of a data set (represented by a box - plot) is calculated as the difference between the maximum value and the minimum value, i.e., \( \text{Range}=\text{Maximum}-\text{Minimum} \).

Step2: Find the range of the Morning box - plot

From the box - plot for the Morning:
Let's assume the minimum value (\( \text{Min}_{\text{Morning}} \)) is 3 (from the left - most whisker) and the maximum value (\( \text{Max}_{\text{Morning}} \)) is 15 (from the right - most whisker).
Then the range of the Morning box - plot, \( R_{\text{Morning}}=\text{Max}_{\text{Morning}}-\text{Min}_{\text{Morning}} = 15 - 3=12 \).

Step3: Find the range of the Afternoon box - plot

From the box - plot for the Afternoon:
Let's assume the minimum value (\( \text{Min}_{\text{Afternoon}} \)) is 4 (from the left - most whisker) and the maximum value (\( \text{Max}_{\text{Afternoon}} \)) is 16 (from the right - most whisker).
Then the range of the Afternoon box - plot, \( R_{\text{Afternoon}}=\text{Max}_{\text{Afternoon}}-\text{Min}_{\text{Afternoon}}=16 - 4 = 12 \).

Answer:

The range of the Morning box plot is the same as the range of the Afternoon box plot.