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Chebyshev's Theorem for a Sample of Scores on a Psychology Exam

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For a particular sample of 77 scores on a psychology exam, the following results were obtained.
First quartile = 44 Third quartile = 71 Standard deviation = 6 Range = 45
Mean = 64 Median = 57 Mode = 92 Midrange = 60

I. What score was earned by more students than any other score? Why?
II. What was the highest score earned on the exam?
III. What was the lowest score earned on the exam?
IV. According to Chebyshev's Theorem, how many students scored between 40 and 88?
V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 46 and 82?

Please show all of your work.

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Solution Preview

(a) 92 was the score obtained by students more than any other score. This is because mode is 92.

(b) Let the highest and lowest scores be H and L respectively. We have H ...

Solution Summary

This solution explains the mode, how to solve for highest and lowest score using the midrange and range, the number of students that scored between 40 and 88 according to Chebyshev's theorem and the number of students that scored between 46 and 82 according to the Empirical Rule.