Question

the box plot shows the distribution of the scores on a science test. decide whether each statement is true or false. the range of the data set is 12. true the median test score is 84. false about half the test scores are between 84 and 91. ?

Explanation:

Step1: Recall box - plot properties

In a box - plot, the range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). The median is the middle value of the data set. The box in the box - plot represents the inter - quartile range (\(IQR\)), and about \(50\%\) of the data lies within the box.

Step2: Analyze the first statement

From the box - plot, assume the minimum value \(x_{\text{min}} = 82\) and the maximum value \(x_{\text{max}}=96\). Then \( \text{Range}=96 - 82=14
eq12\). So the statement “The range of the data set is 12” is False.

Step3: Analyze the second statement

The median is the line inside the box. Looking at the scale, the median is not 84. If we assume the scale (each tick mark represents 2 units), the median is in the second half of the box (not at 84). So the statement “The median test score is 84” is False.

Step4: Analyze the third statement

The box in a box - plot contains about \(50\%\) of the data. The lower end of the box is approximately 84 and the upper end of the box is approximately 91. So about half the test scores are between 84 and 91. This statement is True.

Answer:

• “The range of the data set is 12”: False
• “The median test score is 84”: False
• “About half the test scores are between 84 and 91”: True