Question 242761: For a particular sample of 50 scores on a psychology exam, the following results were obtained.
First quartile = 39 Third quartile = 71 Standard deviation = 10 Range = 62
Mean = 62 Median = 61 Mode = 68 Midrange = 69
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 42 and 82?
- Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 42 and 82?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For a particular sample of 50 scores on a psychology exam, the following results were obtained.
First quartile = 39 Third quartile = 71 Standard deviation = 10 Range = 62
Mean = 62 Median = 61 Mode = 68 Midrange = 69
Answer each of the following; show all work.
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- What score was earned by more students than any other score? Why?
Mode = 68
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- What was the highest score earned on the exam?
Median + (1/2)range = 61+31 = 92
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- What was the lowest score earned on the exam?
Median - (1/2)range = 61-31 = 30
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- According to Chebyshev's Theorem, how many students scored between 42 and 82?
(42-62)/10 = -2 ; (82-62)/10 = 2
Within 2 std's of the mean you have at least 1-(1/2)^2 = 75% of the data
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- Assume that the distribution is normal. Based on the Empirical Rule, how many students scored between 42 and 82?
P(42 < x < 82) = P(-2 < z < 2 ) = 0.9545
0.9545*50 = 47.72
Rounding up you get 48
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Cheers,
Stan H.
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