Standard Deviation

The standard deviation is a common measure of variability of the data from a group or population. This is applied in statistics or probability in which the dispersion or the spread of the data gathered from the population is being analyzed. To represent the standard deviation in formulas, the lowercase sigma symbol is being used.

This method of measurement of data was formulated in the 1860s by the mathematician Galton. Since then, the standard deviation remains to be the most common technique in measuring the dispersion. The computation for the standard deviation may be used for random variables, probability distribution or population.

Standard deviation is defined as the square root of the variance or the RMS (root-mean-square) deviation from the mean of the data. A small standard deviation means that many of the data are not far from the mean or the average of the data. A high standard deviation value would mean that the data is widely dispersed and are far from the mean. A standard deviation equal to zero means that all the gathered data are equal. The advantage of using standard deviation over the variance as a measure of the variability of data is that the standard deviation is expressed in the same unit as the data being analyzed.

In populations when it is not possible to get all the data for analysis or when the data is not available, the standard deviation for the population may be computed using the values gathered from the sample by using the formula for the modified standard deviation.