What is Standard deviation?

Standard deviation is a measure of how spread out the numbers in a dataset are. It tells you how far each value is from the mean. For example, in the numbers 4,7,6 the standard deviation measures the amount of variation of the values of a variable about its mean.

How to use the standard deviation calculator?

Enter the numbers separated by commas.

Choose an option from "sample standard deviation."

After entering the value, you click on calculate, and in seconds, you will see the result.

Step-By-Step Solution (Sample)

Step 1: Given numbers: 4, 7, 6
Step 2: Calculate mean = 17 ÷ 3 = 5.6667
Step 3: Calculate squared differences from mean:
(4 - 5.6667)² = 2.7778
(7 - 5.6667)² = 1.7778
(6 - 5.6667)² = 0.1111
Step 4: Sum of squared differences = 4.6667
Step 5: Sample variance = sum ÷ (n-1) = 4.6667 ÷ 2 = 2.3333
Step 6: Standard deviation = √variance = √2.3333 = 1.5275
Result: Standard deviation = 1.5275, Variance = 2.3333, Mean = 5.6667, Type = Sample

Choose an option from "population standard deviation"

Example 1: Population Standard Deviation:
Dataset: 8, 2, 2, 2, 4, 5, 5, 7, 9
After entering values, click calculate and see results in seconds.

Step-By-Step Solution (Population)

Step 1: Given numbers: 8, 2, 2, 2, 4, 5, 5, 7, 9
Step 2: Calculate mean = 44 ÷ 9 = 4.8889
Step 3: Calculate squared differences from mean:
(8 - 4.8889)² = 9.6790
(2 - 4.8889)² = 8.3457
(2 - 4.8889)² = 8.3457
(2 - 4.8889)² = 8.3457
(4 - 4.8889)² = 0.7901
(5 - 4.8889)² = 0.0123
(5 - 4.8889)² = 0.0123
(7 - 4.8889)² = 4.4568
(9 - 4.8889)² = 16.9012
Step 4: Sum of squared differences = 56.8889
Step 5: Population variance = sum ÷ n = 56.8889 ÷ 9 = 6.3210
Step 6: Standard deviation = √variance = √6.3210 = 2.5142
Result: Standard deviation = 2.5142, Variance = 6.321, Mean = 4.8889, Type = Population

How does the standard deviation calculator work?

The MathCalc standard deviation calculator finds the mean of the dataset. After that, it finds the variance. If you find the population standard deviation, it divides the variance by n, and if you find the sample standard deviation, it divides the variance by n-1. And then, takes the square root of the final value to get the standard deviation.

Why use the MathCalc standard deviation calculator?

Get quick results

Everyone can get accurate and instant results with the help of the MathCalc standard deviation calculator. Enter the values and choose an option. After entering the values, click on calculate, and in seconds, you will see the results. Example: Find the standard deviation of 2, 4, 8. Just enter the values and get quick results.

Reduce Human Error

The accurate formulas of MathCalc standard deviation ensure you always get the correct standard deviation. Example: If you find the standard deviation of 24, 28, 29 by hand, it is easy to mess up, but this calculator gives you an accurate result in seconds.

Multiple Functions

This MathCalc calculator also calculates the mean, variance, and step-by-step breakdown.

FAQ

What’s the difference between population and sample standard deviation?

The population uses all data points and divides by n. Sample uses a subset and divides by (n – 1).

Can I use decimals and negative numbers?

Yes, you can enter decimals and negative numbers in a calculator.