Mathematics
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Standard Deviation Calculator

Compute the standard deviation, variance, mean, and sum of your data set instantly. Handles both entire group (population) and partial subset (sample) algorithms.

Data Set 1

Data Entry

What kind of data is this?

Statistical Output

Standard Deviation (σ)

4.90

Variance (σ²)24.00
Average (Mean)18.00
Sum of Values144.00
Data Count (N)8
Margin of Error (SE)1.73

Empirical Rule (68% Check)

DATASPREAD
Within 1 Std Dev (38%)
3 points
Outside 1 Std Dev (63%)
5 points

Data Distribution Plot

24.3Avg8.7
Data Points
Average (Mean)
± 1 Std Dev Zone

Step-by-Step Variance Table

Point #Value (x)Distance (x - μ)Squared (x - μ)²
110.00-8.0064.00
212.00-6.0036.00
323.005.0025.00
423.005.0025.00
516.00-2.004.00
623.005.0025.00
721.003.009.00
816.00-2.004.00

Complete Math Guide

Mastering the Standard Deviation Calculator

Welcome to the most precise and user-friendly Standard Deviation Calculator available online. When dealing with raw numbers, finding the average (mean) is only half the battle. If I tell you the average temperature of two cities is 70°F, you might think they have identical climates. However, if one city is always exactly 70°F, and the other swings between 40°F and 100°F, their statistical realities are vastly different.

Standard deviation is the mathematical tool that solves this problem. It is a strict measure of variation or dispersion within a set of data. This calculator instantly computes exactly how scattered your data points are from the center. It eliminates the tedious process of calculating individual squared differences manually, providing not just the final result, but a full variance table and a visual distribution plot.

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