Standard Deviation Calculator

Standard Deviation (σ) Calculation


Perform or verify the results of standard deviation (σ) and population standard deviation (PSD) calculation by using this standard deviation calculator. By using it, users can calculate SD, SD variance, PSD and PSD variance by supplying the input values of a data set. Unlike other calculators, this advanced tool provides you the complete calculation instead of simply providing you the answers.


Standard Deviation can be calculated from the below formula
Standard Deviation Formula & Calculation

The formula to calculate Population SD is:
PSD - Population Standard Deviation Formula & Calculation

The formula to calculate Variance is:
Variance Formula & Calculation

The formula to calculate Mean is:
Mean Formula & Calculation


The standard deviation is a common measure of the spread of a data set or distribution and broadly used in statistics and probability theory for the assessment of variability or diversity employed. It explains how much variation or dispersion from the average mean, or expected value. A low σ shows that the data points tend to be very close to the mean, whereas high σ shows that the data are spread out in excess of a large range of values. When it comes to statistical theory standard deviation calculation is more important and highly in demand. The square root of the variance is called the Standard Deviation, usually denoted by s or σ. It is often abbreviated to SD. The variance is calculated from the squares of σ of observations.

The mean is a measure of central tendency value for a distribution, is the same as the average of the data set. It's also popularly known as arithmetic mean or average often referenced along with the standard deviation; which describes the central location of the data and the σ describes the spread. Central limit theorem states that regardless of the data set approaching a normal distribution when the data set is large. Most of the calculations made regarding normal distribution therefore, the normal distribution is important in statistics theory.

In many applications it is necessary to calculate the SD or PSD or SD Variance or PSD Variance or both for making scientific implication from the summarized data of a given data set. Therefore, it is an important measure in data analysis to find out common measure of spread of data set. The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing the data to understand theory of probability and statistics. When it comes to verify such calculations or perform such calculations online, this advanced standard deviation calculator may assist you to compare your results or get your calculations done.

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