Standard Deviation

Statistics provides you with tools to analyze any kind of data. It is a science which has a broad range of application from the natural sciences to social sciences. Statistics is mathematics applied to analysis of large amount of data gathered through experimentation and surveying. One of the most important of math terms, when it comes to data analysis is standard deviation. It is one of the most important tools used in statistical analysis and probability theory.

Definition

In pure statistical jargon, the standard deviation of any set of data points is an exact measure of the amount of dispersion that exists around the mean or average value. I assume that you are already familiar with what is mean in math. It can be defined as the square root of a ratio between 'sum of squares of differences between each data point and the mean' and the 'total number of data points minus one'.

Formula

The standard deviation symbol is 'σ'. For a data set with a total of N points, where X_Mean is the average value is given as:

σ = √[{Σ_n=1^N (x_n - X_Mean)²}/{N - 1}]

Calculation

The first step in the process is to calculate the mean of the data set. To do so, you must add up all the data points and divide the whole sum by the total number of data points.

The next step is to calculate the difference between each data point and mean of the whole set, square each difference value and then add all of them together. Then divide the sum of the difference squares by (N-1), where N is the total number of data points. Take a square root of the quotient you derive from the earlier calculation. This is the value of standard deviation, for the set.

Standard deviation of any data set is a parameter, which provides you a clear idea of how widely are data points spread around the mean value. The more precise experiment results are, lower will be the deviation. The peak value of the graph drawn of such a data set will be more pointed.