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.

#### Discrete random variable mean value & variance calculator

Enter weight or probability and data number in each row:

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 determining the standard deviation of big data is a long process. The best way is to use the **Online Standard Deviation Calculator** with mean value, variance, and formula.

#### What is Standard Deviation?

To measure the variation or dispersion of some values from a point in a given data we use population and sample standard deviation calculator. 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. If the value of Standard Deviation is lowest then it is likely to be a mean value and vice versa. One of the best use of this is to know the margin of error.

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

## Applications of Population and Sample Standard Deviation Calculator

- Industries perfectly make use of mathematics behind SD. We can use it for production quality. As 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.
- Weather forecasting also implements a deviation calculator. It is used for calculating differences of temperature in various places. Also, it is useful for reporting some abnormal temperature changes.
- Finance is yet another field that uses this calculator. Mostly it’s used for calculating the risks in trading. For measuring the price fluctuations occurring every time. The finance study is incomplete without statistics.

More fields like sports, science, and many others 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 awaiting section. So, let’s know what is the mathematics behind it. We have learned the uses and applications of standard deviation. Now it’s time to know the calculation and formula.

This 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:

We have got our Mean (μ) = 6

Secondly, subtract each value in the sequence with the mean value. Then square the result. Therefore, the equation will something look like (x_{i} – 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 it.

#### Sampled Standard Deviation Calculation

Sample Mean Formula:

Sample SD Formula:

#### Discrete Random Variable SD Calculation

Variable Mean Formula:

Discrete Random Variable SD Formula:

### How to Use Mean/Variance Calculator?

We have covered the mathematics behind the standard deviation calculator. So, let’s know how we can use the calculator for measurement.

Most importantly this service will only work online. So, make sure you have a device that can use the Internet. And also a stable internet connection. Secondly, open your browser and go to our tool website and follow the below steps.

In the input box enter all the numbers separated by a comma or space. Then you can enter any type of data in the box (Population or Sample). After that click on the “Calculate” button to run the tool mechanism. Finally, as a result, you will get the deviation results very quickly.

Therefore, population data is the type of data that contains measurable values. Whereas sample data contains a large population data defined by a sample. A sample statement will provide the whole population data. Choose the one which suits your information and then proceed to calculate.