Question 16

The highest score that the bottom 25% of students scored is 59.

This score represents the first quartile in the distribution of the math test scores, indicating that 25% of the students scored below this value.

A) 54

This option is incorrect because 54 is below the first quartile and does not represent the highest score within the bottom 25% of students. The first quartile is defined as the score below which 25% of the data falls, and 54 does not fulfill this criterion.

B) 59

This option is correct as it accurately reflects the highest score that falls within the bottom 25% of students. In a box plot, the first quartile is the value separating the lowest 25% of the dataset from the rest, making 59 the appropriate answer.

C) 76

76 is incorrect because it is significantly higher than the first quartile. This score represents a higher percentile in the distribution, indicating that it is not part of the bottom 25% of scores.

D) 81

This option is also incorrect as 81 is well above the first quartile threshold, indicating that it is part of a higher percentile than the bottom 25%. Therefore, it cannot represent the highest score for this group of students.

Conclusion

The correct answer, 59, is definitively right as it accurately indicates the highest score of the bottom 25% of students based on the box plot. All other options fail to represent scores within this quartile, as they either fall below or above the required threshold, confirming that 59 is the accurate value for this statistical measure.