# Standard Deviation

While we use percent error to dictate how far we off in class, there are far more efficient ways of defining the error of the set. Standard deviation, for example, given a value, will give rise to numbers that fall within one S.D., two S.D. and so on.

"One can find the standard deviation of an entire population in cases (such as standardized testing) where every member of a population is sampled. In cases where that cannot be done, the standard deviation σ is estimated by examining a random sample taken from the population. An estimator for *σ* used when sample size is very large is the standard deviation of the sample, denoted by *s** _{N}* and defined as follows:"

This method is effective for creating intervals for which certain points would have to lie within and give us the ability to decide on percent error for an entire group of values. The closer the value of S.D. approaches 0, the less the error percent is.

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