Question

multiple choice 1 point
a data set contains student test scores.

• the median test score is 75 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 45 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.

Explanation:

• Range: Range = Highest score - Lowest score = 40, but we don’t know either value individually, so A (lowest=45) and B (highest=95) can’t be confirmed (they only work if highest=85 or lowest=55, which isn’t given).
• Quartiles: The median (Q2) is 75, third quartile (Q3) is 85. By definition, Q3 is the value where ~75% of scores are below it and ~25% are above. This means ~25% of scores are between Q2 (75) and Q3 (85).
• Option C: There’s no info about Q1 (first quartile), so we can’t confirm 25% are below 55.

Answer:

D. About 25% of the test scores are between 75 and 85 points.