Help with a standard deviation question

[jw_gino]

Can someone please explain how you would find the answer to this question?

For a certain examination, a score of 58 was 2 standard deviations below the mean, a score of 98 was 3 standard deviations above the mean, what was the average score?

[jnelson0612]

Can someone please explain how you would find the answer to this question?

For a certain examination, a score of 58 was 2 standard deviations below the mean, a score of 98 was 3 standard deviations above the mean, what was the average score?

Sure! Let's let "x" stand for the standard deviation. Thus:
98 = mean + 3x
58 = mean - 2x

Subtract the second equation from the first. I get 40 = 5x. Thus, x, or the standard deviation, must be 8. Let's check it out.

If I add 2(8) to 58, that gives me 74.
If I subtract 3(8) from 98, that gives me 74.

We're good! The mean is 74.

[rakshaki]

I solved this as a weighted average problem.

2(98)+3(58)/5=mean

Thus mean = 74. Was I lucky or is my approach legitimate?

Thanks
Rakshaki

[RonPurewal]

Please search the forum before posting. Thanks.

post17297.html#p17297

[RonPurewal]

I solved this as a weighted average problem.

2(98)+3(58)/5=mean

Thus mean = 74. Was I lucky or is my approach legitimate?

Thanks
Rakshaki

Conceptually this situation has nothing in common with weighted averages, so, technically, you got "lucky".

On the other hand, both this type of situation and the weighted average ultimately give you the point that's 2/5 of the way from one endpoint to the other one (albeit for entirely different reasons), so it's not a coincidence that the answers work out the same. (In other words, these aren't "special" numbers; the same coincidence will occur with other numbers.)

[RonPurewal]

If you have other questions, please post them at the link above. Thanks.