A data set contains student test scores.
- The median test score is \( \mathbf{7 5} \) points.
- The third quartile value is 85 points.
- The range of the test scores is 40 points.
Which statement about the test scores in the data set is most likely true?
A. The lowest test score is \( \mathbf{4 5} \) points.
B. The highest test score is 95 points.
C. About \( 25 \% \) of the test scores are less than 55 points.
D. About \( 25 \% \) of the test scores are between 75 and 85 points.
Answer
\text{To satisfy the range, only option B is possible: Max score} = 85 + 40 = 125 \Rightarrow \text{Min score} = 125 - 40 = 85
Step 1 ：\text{Median (Q2)} = 75, \text{Q3} = 85, \text{Range} = \text{Max} - \text{Min} = 40
Step 2 ：\text{Since Q3 = 85, at least 75% of scores are below 85}
Step 3 ：\text{To satisfy the range, only option B is possible: Max score} = 85 + 40 = 125 \Rightarrow \text{Min score} = 125 - 40 = 85
