Question

middle school students
elementary school students
which are true statements when comparing the data in the box plots? select three choices.
the data for elementary school are more consistent than those for middle school.
more of the data for middle school lie closer to the median than the data for elementary school.
about 50% of elementary school students watch between 4 and 7 hours of television each week.
about one - half of middle school students watch less than 2 hours of television each week.
on average, middle school students watch less television than elementary school students each week.

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR), which contains 50% of the data. The median is the line inside the box. A smaller IQR indicates more consistent data.

Step2: Analyze consistency

The IQR for elementary school students is \(7 - 4=3\), and for middle school students, it is larger. So, the data for elementary school are more consistent. The first statement is true.

Step3: Analyze middle - school data proximity to median

There is no evidence to suggest that more of the middle - school data lie closer to the median than elementary - school data.

Step4: Analyze elementary - school IQR

For elementary school students, the box ranges from 4 to 7. Since the box represents the middle 50% of the data, about 50% of elementary school students watch between 4 and 7 hours of television each week. This statement is true.

Step5: Analyze middle - school lower half

The lower half of the middle - school data is not all below 2 hours. The median for middle - school students is greater than 2.

Step6: Analyze average viewing

The median for middle - school students is around 4 and for elementary school students is around 5.5. So, on average, middle - school students watch less television. This statement is true.

Answer:

The data for elementary school are more consistent than those for middle school.
About 50% of elementary school students watch between 4 and 7 hours of television each week.
On average, middle school students watch less television than elementary school students each week.