The study of statistics is fascinating, and we want to help you discover this feeling. One of the especially useful topics is the standard deviation, as it gives you great information to observe and compare data. In this article, you will find our online standard deviation calculator, where you will learn how to obtain it step by step.

## Standard Deviation Calculator

## What is Standard Deviation?

Standard deviation is a statistical measure of the dispersion or variation of a set of data. This dispersion tells us how the data are distributed about the mean.

To calculate the standard deviation, we will use the following formulas, depending on whether the data to evaluate corresponds to the population or if it only represents a sample:

#### (a) Population standard deviation:

#### (b) Sample standard deviation:

Where:

: Population standard deviation.**Ïƒ**: Sample standard deviation.**s**: Mean.**xÌ„**: Number of evaluated values.**N**: Each of the values.**x**_{i}

## How to use the online standard deviation calculator?

To calculate the standard deviation using our application, we will follow the following steps:

- Choose the decimal number notation and the data separator by selecting the corresponding options.
- Enter the set of values to evaluate.
- Click on Solve.
- Next, you will be able to visualize the detail of the calculations performed.

To understand it better, we will see its use with an example:

### Example of standard deviation calculation

Find the standard deviation of the following numbers:

12, 15, 17, 20, 30, 31, 43, 44, 54

### Solution

We enter the values in the tool:

When clicking on “Solve” we will obtain the following:

**Population Standard Deviation:** 13.9771

**Sample Standard Deviation:** 14.8249

**Population Variance:** 195.358

**Sample Variance:** 219.7778

**Mean:** 29.5556

**Count of Data:** 9

According to the data of the problem we have:

266*Î£xáµ¢*Â =Â9*N*Â =Â266/9 = 29.5556*xÌ„*Â =Â

x_{i} |
x_{i} – xÌ„ |
(x_{i} – xÌ„)^{2} |
---|---|---|

12 | -17.5556 | 308.1991 |

15 | -14.5556 | 211.8655 |

17 | -12.5556 | 157.6431 |

20 | -9.5556 | 91.3095 |

30 | 0.4444 | 0.1975 |

31 | 1.4444 | 2.0863 |

43 | 13.4444 | 180.7519 |

44 | 14.4444 | 208.6407 |

54 | 24.4444 | 597.5287 |

Î£xáµ¢ = 266 | xÌ„ = 266/9 = 29.5556 | Î£(xáµ¢ – xÌ„)Â² = 1758.2223 |

At the end, you will find the option to copy the problem link so that you can see the results without having to re-enter the data. It is beneficial to share the solutions with a colleague.

Finally, if you want to find other measures of dispersion or central tendency, you can visit the following options:

- Mean Absolute Deviation Online Calculator.
- Variance Online Application.
- Online calculator for mean, median, mode, and range.

## Final Reflection

As you can see, knowing about standard deviation is extremely important for statistical analysis. Our calculator is an excellent tool that will help you deepen everything related to this statistical concept.