8
QuizMultiple Choice

Range and Interquartile Range

Question 8 • Concepts in Probability and Statistics A

Mrs. Juarez graded ten English papers and recorded the scores.92, 95, 100, 62, 88, 90, 100, 96, 89, 98Which statements are true? Check all that apply.

Answer
A
The range of scores is 38.
B
Without the outlier, the range of scores would be 12.
C
The outlier impacts the range more than it impacts the interquartile range.
D
The interquartile range is 9.
E
The interquartile range is 4.
F
Without the outlier, the interquartile range would be 9.5.

Explanation

In order, the scores are 62, 88, 89, 90, 92, 95, 96, 98, 100, 100. The range is 100 − 62 = 38; without 62, it is 100 − 88 = 12. The lower and upper halves have medians 89 and 98, so the interquartile range is 98 − 89 = 9. Without 62, the quartiles are 89.5 and 99, giving an interquartile range of 9.5. Thus, the outlier changes the range much more than the interquartile range.

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