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Say, mean score = M and standard deviation = Dpsm12se wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
A little background on units of standard deviation:psm12se wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
A 74
B 76
C 78
D 80
E 82
There's no need to solve a two equations/two unknowns problem here; if 58 and 98 are five standard deviations apart, the standard deviation is (98-58)/5 = 8. Thus the mean is 58 + (2)(8) = 74.psm12se wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
Another perspective.psm12se wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
A 74
B 76
C 78
D 80
E 82
Iceman, your method still leaves 2 answer choices...Ian solved it exactly the way I did & it took me less than a minute to work through the problem (ie...allows you to solve the problem efficiently, giving you more time to work on complicated problems)...Assuming that you understand what standard deviation means, you can simply obtain the range, which is 40 (98-58 = 40) and we know that we are 2 sd below and 3 above, so that means we have a 5 sd spread which we divide into 40, giving us a sd of 8. Verify this works by subtracting sd*3 (24) from the high score of 98 and making sure that is equal to adding sd*2 (16) to the low score of 58 and you get 74 in both cases, so the answer is A.The Iceman wrote:Another perspective.psm12se wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
A 74
B 76
C 78
D 80
E 82
Imagine this sentence appears as the last question on the GMAT and you have only 15-20 secs to mark the answer.
Just take the avg of the two numbers avg(58,98) = 78. Now our ans must be less than 78 as the mean has to be farther from 98 and closer to 58.
Cking6178, I think you misinterpreted me. I never provided the solution anyway. All i told was that if faced in a time bound situation you could easily get rid of 3 options and make an educated guess.cking6178 wrote:Iceman, your method still leaves 2 answer choices...Ian solved it exactly the way I did & it took me less than a minute to work through the problem (ie...allows you to solve the problem efficiently, giving you more time to work on complicated problems)...Assuming that you understand what standard deviation means, you can simply obtain the range, which is 40 (98-58 = 40) and we know that we are 2 sd below and 3 above, so that means we have a 5 sd spread which we divide into 40, giving us a sd of 8. Verify this works by subtracting sd*3 (24) from the high score of 98 and making sure that is equal to adding sd*2 (16) to the low score of 58 and you get 74 in both cases, so the answer is A.The Iceman wrote:Another perspective.psm12se wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
A 74
B 76
C 78
D 80
E 82
Imagine this sentence appears as the last question on the GMAT and you have only 15-20 secs to mark the answer.
Just take the avg of the two numbers avg(58,98) = 78. Now our ans must be less than 78 as the mean has to be farther from 98 and closer to 58.
The explanation is wordy, but the math is quick and painless.
Great solution, Ian. I was totally fixated on the algebraic approach. Fortunately, that approach isn't much longer than just applying some common sense (as you did).Ian Stewart wrote:There's no need to solve a two equations/two unknowns problem here; if 58 and 98 are five standard deviations apart, the standard deviation is (98-58)/5 = 8. Thus the mean is 58 + (2)(8) = 74.psm12se wrote:For a certain examination, a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviations above the mean. What was the mean score for the examination?
Yes, I like your image, especially if you turn it so that 2x is below 3xbuzzdeepak wrote:Here is how I solved (I like to "see" things and try to draw pictures or tables as and when I can - nothing fancy, just quick and dirty)
[/img]
So, 5x = 98-58 = 40
x = 8
Therefore, 2x = 16
The answer, therefore, is 58+16 = 74
Nothing different than what all the experts have said earlier, just another way (sometimes a picture says a thousand words)
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