standard deviation vs percentiles

Simple answer: No. The standard deviation is a measure of the spread of the data. It has nothing to do with percentiles. However, the number of standard deviations above/below the mean is related to percentiles.

Here's something from the link below.
(+/-) One standard deviation away from the mean accounts for somewhere around 68 percent of the people in this group. (+/-) Two standard deviations away from the mean account for roughly 95 percent of the people. And (+/-) three standard deviations account for about 99 percent of the people.

http://www.robertniles.com/stats/stdev.shtml

So, if you're one standard deviation above the mean, you scored higher than 68 + (100-68)/2 percent of the population.

percentiles
Thanks for responding. You said:

"So, if you're one standard deviation above the mean, you scored higher than 68 + (100-68)/2 percent of the population."

And 68 + (100-68)/2 = 84.13 ... and aren't you then in the top 16 percentile (approximately)????

Why do you say that standard deviation has nothing to do with percentile?

If indeed that is true, how do you measure percentile?

If my recollection of statistics is correct:

Standard deviation is a way to normalize the data. That is, a particular measure may have a very flat or very sharp peak/curve. You then can then fit the data to a "normal" distribution (bell curve).

You can use standard deviations to calculate the percentage of the data that falls withing the deviation from the average.

"And 68 + (100-68)/2 = 84.13 ... and aren't you then in the top 16 percentile (approximately)???? "

One standard deviation contains (approximately ) 68% of the population. (The 39% just above average and the 39% just below average.) You are correct that if you are one standard deviation above average that you are in the upper 16%. You are above the 68% within the standard deviation and the lowest 16%.

I would also suggest that you post this question to the Science and Math forum.

According to this site, there isn't a formula to provide what you want. Go to
http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm
and check out Percent Point Function (just a few lines). Click on the link for a slightly larger discussion. I believe the graph labeled 'Normal PPF' is what you're after.