Problem Solving

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?

not sure if this can be solved.

what are the answer choices?

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

I don't know if we can calculate Mean from Standard deviation

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.

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.