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Standard deviation

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by danjuma » Sat Sep 25, 2010 11:50 am
For a certain examination a score of 58 was 2 standard deviation below the mean and a score of 98 was 3 standard deviation above the mean. What was the mean score?
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by Gurpinder » Sun Sep 26, 2010 7:02 am
not sure if this can be solved.

what are the answer choices?
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by sason » Sun Sep 26, 2010 7:45 am
IMO the answer is 74

let the sd be x
now 58 is two sd below the mean ... and
98 is three sd above the mean
so the diff between 98 and 58 is 5sd
i.e.
98-58 = 5 sd => 5x=40 => x=8
Hence the mean is
58+ 2*x= 74 or 98-3*x= 74
So the answer is 74

Correct me if wrong ...
btw what's the OA ...

regards
sason
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by nasir » Sun Sep 26, 2010 5:49 pm
I don't know if we can calculate Mean from Standard deviation
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by limestone » Sun Sep 26, 2010 7:05 pm
IMO, we cannot calculate mean from standard deviation. To do so we must know all the values of the range, or the sum & the total items in the range.
However, in this case, mean and standard deviation have been pre-calculated, though they are still unknown to us. The given information gives us that 58 is 2 standard deviation (SD) less than mean, and 98 is 3 SD more than mean. So 98-58 = 5SD is correct. Then SD =8 and mean = 58+8*2 = 74.
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by artistocrat » Tue Oct 05, 2010 4:08 pm
If we understand a deviation as an interval this question is dead simple, since there are 40 percentage points between 58 and 98 divided by 5 intervals, which leaves us with an 8-point interval. 2 8-point intervals over 58 is 74.
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