STANDARD DEVIATION

Standard Deviation

Standard Deviation

In probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though practically less robust than the expected deviation or average absolute deviation.

Standard Deviation is a measure of how results are distributed within a range of possible outcomes. This score is useful when comparing averages - for example two scores may have the same average of '50' with one comprising of results entirely between 45 and 55 and the other having results ranging from 1 through to 100. The second set of scores is more widely distributed than the first, which will be reflected in a higher standard deviation score.

It shows how much variation there is from the "average" (mean) (or expected/budgeted value). It helps detect tampering of data. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

In many natural processes, random variation conforms to a particular probability distribution known as the normal distribution, which is the most commonly observed probability distribution. Mathematicians de Moivre and Laplace used this distribution in the 1700's. In the early 1800's, German mathematician and physicist Karl Gauss used it to analyze astronomical data, and it consequently became known as the Gaussian distribution among the scientific community.

The standard deviation therefore is simply a scaling variable that adjusts how broad the curve will be, though also appears in the normalizing constant to keep the distribution normalized for different widths.

If a data distribution is approximately normal then the proportion of data values within z standard deviations of the mean ...