Work out the mean Example 2 continued : 9 - 6. It can be calculated analytically and is therefore reliable. Retrieved 30 May 2015.

It is unaffected by any form of unexpected Deviation.

The higher the standard deviation, the more spread out the values, while a lower standard deviation indicates that the values tend to be close to the mean. For a population: where N is the population size, μ is the population mean, and x i is the i th element in the set. Calculating the formula by hand is very time-consuming and there is a high risk of making a mistake.

NextWith today's technology, you usually solve standard deviation calculations through computer programs or spreadsheets.

When dealing with the amount of deviation in their portfolios, investors should consider their tolerance for and their overall investment objectives. In the standard deviation formula for a population,.

The difference between the actual and average value is known as dispersion or variance.

This is the process of converting raw data through various operations, into a piece of meaningful information.

NextAs such, the "corrected sample standard deviation" is the most commonly used estimator for population standard deviation, and is generally referred to as simply the "sample standard deviation.

There are other formulas for calculating standard deviation depending on how the data is distributed.

NextThe excess kurtosis may be either known beforehand for certain distributions, or estimated from the data.

Population deviation is the most common. When your data is closely related to the average, it has a low standard deviation, meaning your data is very reliable.

Standard deviation is always positive and is denoted by σ sigma.

} As explained above, while s 2 is an unbiased estimator for the population variance, s is still a biased estimator for the population standard deviation, though markedly less biased than the uncorrected sample standard deviation. Standard deviation is used throughout statistics, and in many cases is a preferable measure of variability over because it is expressed in the same units as the collected data while the variance the square of the standard deviation has squared units. When the average of the squared differences from the mean is low, the observations are close to the mean.

In cases where that cannot be done, the standard deviation σ is estimated by examining a random sample taken from the population and computing a of the sample, which is used as an estimate of the population standard deviation.