Standard Deviation Calculator

Standard Deviation Calculator will help you to calculate population and sample standard deviation(SD) with variance and mean value online.

First of all, enter the values with commas (e.g: 1,2,4,7) or spaces (e.g: 1 2 4 7) and press the “Calculate” button.

Enter Values:
Population standard deviation:
Sample standard deviation:
Population variance:
Sample variance:

Discrete random variable mean value & variance calculator

Enter weight or probability and data number in each row:

Probability Data number
Standard deviation:

Standard Deviation Formula | GPA Calculator | Z Score Table | Average Calculator

In the mathematics world, it is an important part of statistics. It is using in various fields like analysis of a given data. Also, it is universally denoted by “σ” (Lowercase Sigma of Modern Greek Alphabet).

Manually solving the standard deviation of big data is a very long process. The best way is to use the Online Standard Deviation Calculator to solve it. As a result, it will give you a mean value, variance, and standard deviation.

Standard Deviation Calculator with Mean Value & Variance

What is Standard Deviation?

Generally, it is used to measure the variation of some values from a point in a given data. Even more, we can use the concepts of mean and variance. Mean can be treated as the median or average of a given sequence of data. One of the best use of this is to know the margin of error.

In addition, it is useful in many fields like finding out the probability. This mean/variance calculator makes all the work easier. Furthermore, the outcome is always correct. In this article, all the calculation steps used in determining the standard deviation of data are also discussed. We have used an advanced algorithm in this calculator.

Applications of Population and Sample Standard Deviation Calculator

  1. Industries are perfectly using mathematics behind standard deviation. Also, we can use it for production quality. It can calculate the minimum and maximum range of the specific aspect in which the product should fall. If however, a product is not in this range then it can be considered for a recheck.
  2. Weather forecasting also implements a variance calculator. It is used for calculating differences in temperature in various places and reporting some abnormal temperature changes.
  3. The finance study is incomplete without statistics. So, finance is yet another field that uses this calculator. Mostly it’s used for calculating the risks in trading. Even more, it is measuring the price fluctuations occurring every time.

Other fields like sports, science and many more are implementing this formula. Even more, it is truly a powerful weapon to calculate the probability of something. Some people can win the jackpots in the lottery if they master it!

Calculation Process

This might be the most awaited section. So, let’s know what is mathematics or calculation behind it.

The Standard Deviation Formula is:

Standard Deviation Formula

We will understand this formula very easily by the following example:

We have data like this: 3, 5, 7, 2, 6, 3, 9, 12, 12, 1

First of all, let’s calculate the mean of this data. Mean (μ) is measured by adding all the values and then dividing it by a number of values. In this case, we have 10 values. So, the mean will be:

Mean/Variance Calculator

We have got the Mean (μ) = 6

Secondly, subtract each value in the sequence with the mean value. Then square the result.

Therefore, the equation will look like this:

(xi – μ)2

Where µ is the mean.

Then do the summation of all the results then divide by the number of terms.

There are some more calculations and formulas that are useful and you have to learn them.

Sampled Standard Deviation Calculation

Sample Mean Formula:

Sample Mean

Sample Standard Deviation Formula:

Sample Standard Deviation

Discrete Random Variable Calculation

Variable Mean Formula:

Variable Mean Calculation

Discrete Random Variable Formula:

Discrete Random Variable Standard Deviation

How to Use Mean/Variance Calculator?

The process is very simple. Just follow the below steps.

  1. First of all, enter the values inside the first textarea.
  2. Values must be separated by a comma(e.g.: 1,2,3,4) or space(e.g.: 1 2 3 4)
  3. After that click on the “Calculate” button.
  4. Finally, as a result, you will get the deviation, variance, and mean results very quickly.
  5. For discrete random variable, you need to enter the “Probability” and “Data number”.
  6. In addition, you can add more rows using “Add Row” button and reset the calculator using “Reset” button.
  7. That’s it.


Population data is the type of data that contains measurable values. Whereas sample data contains a large population data defined by a sample. So, choose the one which suits your information and then proceed to calculate.