arithmetic mean and standard deviation

[patrickgong6688]

The arithmetic mean of a data set is 46 and the standard deviation of the set is 4.Which value is exactly 1.5 standard deviation from the arithmetic mean of the set?
A42 B44.5 C47.5 D.50 E52
The answer is E
I do not know why.Can you give me a explaination?

[adrielfrederick]

Standard deviation is a measure used to indicate the amount of deviation away from the mean.

If I say I am one standard deviation away from the mean I can be at Mean-SD or Mean +SD

In your case 1.5 SD works out to be 6 . Therefore Mean +SD works out to be 52

[jnelson0612]

Yes, just take the standard deviation given (4) multiplied by the number of standard deviations the problem is interested in (1.5). In this case we get 6. Add and subtract that to the mean of 46; we get -1.5 standard deviations at 40 and +1.5 standard deviations at 52.

[patrickgong6688]

Thank you So much! I understand!

[jnelson0612]

Great!