The data on the box plot describes the weight of several students in sixth grade. Which of the following statements are true about the data set? Select all that apply.

One-fourth of the students weigh between 90 and 101 pounds.

One-half of the students weigh between 75 and 90 pounds.

The median weight of the sixth graders is 85 pounds.

One-fourth of the students weigh less than 75 pounds.

One-fourth of the students weigh more than 75 pounds.

The total range of weight is 40 pounds.

One-fourth of the students weigh between 90 and 101 pounds. One-half of the students weigh between 75 and 90 pounds. The total range of weight is 40 pounds.

Explanation:

The statement “One-fourth of the students weigh between 90 and 101 pounds” is true since the box plot shows the middle 50% of the data, which falls within this range.

The statement “One-half of the students weigh between 75 and 90 pounds” is false. The box plot shows that the median weight (50th percentile) is 85 pounds, which means half of the students weigh less than 85 pounds and half weigh more than 85 pounds.

The statement “One-fourth of the students weigh less than 75 pounds” is false. The lower boundary of the box plot (25th percentile) is higher than 75 pounds, indicating that at least a quarter of the students weigh more than that.

The statement “One-fourth of the students weigh more than 75 pounds” is true. The upper boundary of the box plot (75th percentile) is above 75 pounds, indicating that at least a quarter of the students weigh more than that.

The statement “The total range of weight is 40 pounds” is false. The total range can be determined by subtracting the minimum value from the maximum value, which in this case is 101 - 74 = 27 pounds.

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