SOLUTION: Can you please show me how to answer this? For a particular sample of 50 scores on a psychology exam, the following results were obtained. First quartile = 66 Third quartile

Question 332224: Can you please show me how to answer this?
For a particular sample of 50 scores on a psychology exam, the following results were obtained.
First quartile = 66 Third quartile = 92 Standard deviation = 9 Range = 49
Mean = 74 Median = 82 Mode = 83 Midrange = 73
Answer each of the following; show all work.
- What score was earned by more students than any other score? Why?
- What was the highest score earned on the exam?
- What was the lowest score earned on the exam?
- According to Chebyshev's Theorem, how many students scored between 56 and 92?
- Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 56 and 92?

Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
- What score was earned by more students than any other score? Why?
Mode= most frequently occurring score, 83
=====
- What was the highest score earned on the exam?
highest score= midrange + range/2 = 73+49/2=97.5
====
- What was the lowest score earned on the exam?
Lowest score = midrange - range/2 = 73-49/2=48.5
===
- According to Chebyshev's Theorem, how many students scored between 56 and 92?
largest-average=92-74=18
this represent k=18/9=2 standard deviations from the mean
thus CT states that "at least" 1-1/k^2 =1-1/4=75% of the scores will surround the average within 2 standard deviations.
75% of 50 = 37.5 or 38 scores
===
- Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 56 and 92?
if the data is normally distributed, approx 95% of the scores will surround the mean within 2 standard deviations
so.. 95% of 50 =47.5 or approx 48

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