Standard deviation calculator for both sample and population data. Instantly calculate standard deviation, variance, mean, and sum of squares step by step with complete accuracy.

From population to sample standard deviation, our calculator equips you with precise measures for any dataset. Simply input the values in the provided box, but separate them by commas.

Standard deviation (also known as SD) is a terminology used in statistics. This term describes a statistical indicator of how much variation or dispersion is in a group of numbers. Therefore, calculating standard deviation will show how much individual values in a dataset vary from the dataset’s mean (or average). In simple terms, SD indicates how widely apart the data points are from the mean.

A lower standard deviation indicates data points are closer to the mean (or expected value), **μ**. While a higher standard deviation indicates a broader range of values. For detailed and precise calculations of the data set use online standard deviation calculator Now!

Generally, there are two types of standard deviation in Statistics. The following points highlight the essential details about each type:

As the name indicates, this type of standard deviation is suitable for dealing with the entire population. Therefore, the population standard deviation formula is as follows:

**Formula Explanation: **

N = The total number of Values

xi = An individual Value

μ = The population mean

The sample standard deviation is a subset of the population standard deviation. Therefore, this type is only suitable for analyzing a subset or sample of the population. Due to its resemblance, its formula is almost identical with only one addition—it substitutes ‘N-1’ for ‘N’ in the denominator. The sample standard deviation formula is derived by taking the square root of the variance.

- Formula Explanation:
- xi= One sample value
- x̄ = The sample mean
- N= The sample size

Calculating standard deviation manually takes a lot of time. However, our standard deviation calculator has simplified this process. Whether

you want to calculate the population or sample variant, you can rely on this web utility.

It provides a step-by-step method to find standard deviation for both data types.

Enter the numbers in the specified text box. But make sure to separate each entry through a comma.

Click on the ‘Calculate’ button. Doing so our standard deviation calculator runs its algorithm for the entered values.

In a flash, our SD calculator will display the accurate results.

Review the step-by-step guide for better understanding.

This calculator is famous because of its feature-rich nature. The following points shed light on some of those features:

The UI designers of this free standard deviation calculator have considered ease of use when designing its interface. This is why the tool features a simple and intuitive UI that makes it easier for users to input their data and obtain results.

Our developers have programmed the functionality of this SD calculator by collaborating with expert statisticians. Therefore, the tool ensures accurate calculations every time.

This online calculator for standard deviation uses algorithm-based functionality to process the entered values swiftly. Its instantaneous result-generation capability will save valuable time and effort for its users.

Our online standard deviation calculator doesn’t ask its users for money. The entire functionality is accessible for free. So, you don’t need to spend a single dime on any sort of fancy statistics calculator anymore.

You can use our standard deviation calculator to find standard deviation and assess dispersion and variability for various data types, like categorical, numerical, and ordinal.

Our standard deviation calculator can help you to calculate standard deviation conveniently. Let’s have a look at the standard deviation example for sample data: **30, 20, 28, 24, 11, 17**

Count, N:6

Sum, Σx:130

Mean, x̄:21.666666666667

Variance, s2: 50.666666666667

So after putting values in the above formula the standard deviation, s: 7.118

Standard deviation is important because it offers insightful information about how data points are distributed around the mean by calculating a dataset’s dispersion or variability. It helps identify trends, assess data reliability, detect outliers, compare datasets, and evaluate risk.

Population standard deviation is suitable for evaluating the entire population. However, the sample standard deviation is handy when dealing with a sample or subset of the population.

Finding the standard deviation can be quite challenging. So the SD calculator makes the process easy and gives accurate results with detailed steps. This tool offers the following calculations:

- Variance
- Standard Deviation
- Mean
- Sum of Squares