For a particular sample of 63 scores on a psychology exam, the following results were obtained.

Question

First quartile = 57 Third quartile = 87 Standard deviation = 9 Range = 51
Mean = 72 Median = 72 Mode = 98 Midrange = 57

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 45 and 99?
V. Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 45 and 99?

Confused!!

Answer 1

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1. Mode

2. (max+min)/2 = 57 (midrange)
max+min = 114
but max-min = 51
Add the two equations.
2(max) = 165, max = 82.5?

3. Continue with 2?

4 & 5. 45 and 99 are mean ± 3 SD. What does that tell you?