Hari -

The standard deviation of a population is a fixed number that you can estimate. The standard error of an estimate of the mean of a population is a value made smaller with increasing sample size n - and also, by the Central Limit Theorem, normality may often be assumed. 

You could do an internet search on "standard deviation," standard error," "confidence intervals," and "Central Limit Theorem" for more information. 

My guess is that you want the standard error, probably of a mean. 

Cheers - Jim

PS - Oops.  I was too quick.   You are dividing that estimated standard error of the estimated mean, by the estimated mean, to get an estimated relative standard error of a mean, sometimes reported instead of a confidence interval about the mean. I was in an organization where we reported the estimated relative standard errors  (RSEs) for estimated totals.  Some may call these RSEs by another name, cvs, coefficients of variation, but that often may refer to a regression parameter instead.  Notation and terminology vary a bit. 

Anyway, an estimated mean or total can be reported with an estimated relative standard error, and then this represents the half-width of a one standard error confidence interval, about 68% when assuming normality. 

Bottom line to your question,  you need the sqrt(n-1) in there if you are looking at the accuracy of an estimated mean.  (If this is "accuracy," and not just "precision," then you need an unbiased estimate of the mean.)

By multiplying by 100, you are expressing your estimated "relative standard error" as a percent.   

There is nothing like THE %error. If you provide such a measure you simply need to explain what it is.

However, the ratio of sigma to mean is known as the coefficient of variation (CV). This is a dimensionless number that can be given as a percent value (CV = sigma/mean, CV% = CV*100%). It describes the variation/dispersion of the values of a variable. The CV is useful to compare the disprsions of variables that are measured on different scales, like if you measure the blood oxygen concentration by a fingertip oximeter or by a chemical titration. The scales have different units, and the dispersion of the measurements can be compared only via the CV.

Sometimes it is helpful to give a range that will contain "most" of the observed values (or yet unobserved values with some "high" confidence). Such an interval is called a prediction interval.

At least to my knowledge, giving %error = ((sigma/sqrt(N-1))/Mean)x100% is uncommon. The part sigma/sqrt(N-1) is known as the standard error (of the mean) and indicated the precision of an estimate (=of the mean). Usually this value is not so simple to interpret directly, and it is better provide an interval with a defined confidence for the estimate (this is called a confidence interval)

As Jim said: %error (no matter how you calculate it, that is, if you refer to the standard error or to the standard deviation), is often not a very meaningful or useful measure. It is hard to interpret, it does not tell us much, and it is likely even misleading when the assumptions we make to interpret this value don't match the reality. It is thus better to provide prediction intervals or confidence intervals, respectively, with a well-defined level of confidence.

In survey statistics, for reporting Official Statistics, RSEs are used, perhaps far more often for reporting estimated totals than estimated means, and RSE is the same thing as cv.  

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons, is a classic that is well written, and he uses the term cv - lower case letters, I don't know why - but I actually agree with those who use the acronym RSE, as it is more descriptive.  RSE: "Relative Standard Error."    It is the standard error relative to the mean, or total, whatever you are estimating.  "Coefficient of Variation" just isn't as intuitive.  But here, it's the same thing.

(Note that in another classic book, Hansen, Hurwitz, and Madow, they even call the square of the RSE the relative variance, or Rel-Var, I think is the way they wrote it, or maybe RelVar.) 

As noted, estimated RSEs are used a great deal when reporting estimated totals for Official Statistics.  When you report thousands of numbers that, for example, an energy analyst wants to see, he/she may have a hard time efficiently viewing all the necessary information if shown in confidence intervals, so they view the point estimates, and with RSEs available, they may know relative accuracy, especially where most important.  I am talking about a great deal of information, not just a few dozen results.  That is why I think it particularly important not to report aggregate results to more digits than are "significant," justifiable by the estimated RSEs and hopefully other information, to quickly give an analyst the overall 'picture.' 

Cheers.

Thank you, Jim!

Thanks for comments!