For a particular sample of 50 scores on a psychology exam, thefollowing results
ID: 2952526 • Letter: F
Question
For a particular sample of 50 scores on a psychology exam, thefollowing results were obtained.Firstquartile = 40 Third quartile = 79 Standard deviation =9 Range = 52
Mean= 67 Median = 71 Mode = 70 Midrange =66
Answereach 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 between40 and 94?
- Assume that the distribution is normal. Based on theEmpirical Rule, how many students scored between 49 and 85?
Explanation / Answer
- 70 is thescore was earned by more students than any other score because itsthe mode of the distribution. Mode is the valuethat occurs the most frequently in a data set. - What wasthe highest score earned on the exam? Range = 52 i.e, Highest score - Lowest score = 52 hence, highest score = 52 + Lowestscore ------------eqn (i) Midrange = 66 hene, (Highest Score + Lowest score)/2 = 66 hence, highest score = 2*66 -Lowest score hence , highest score = 132 -Lowestscore -------------------eqn (ii) from eqn(i) and (ii) we get, 52+Lowest score = 132 -Lowest score hence 2*Lowest score = 132-52 hence, lowest score = 40 putting the above value in eqn (i), highest score = 52 +40 =92 - the lowestscore earned on the exam as per the above calculations is 40
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