Standard Deviation Calculator

Statistic	Value
Standard Deviation (σ)	4.47038869
Count (N)	8
Sum (Σx)	133
Mean (μ)	16.62500000
Variance (σ²)	19.98437500

Calculation Steps:

Variance (σ²):
σ² = [(11 - 16.62500000)² + (9 - 16.62500000)² + (21 - 16.62500000)² + (21 - 16.62500000)² + (17 - 16.62500000)² + (21 - 16.62500000)² + (19 - 16.62500000)² + (14 - 16.62500000)²] / 8
= 159.87500000 / 8
= 19.98437500

Standard Deviation (σ):
σ = √19.98437500
= 4.47038869

Standard Deviation Calculator

The Standard Deviation Calculator helps you quickly find the standard deviation, mean, variance, and other statistics for a set of numbers. Enter your data as comma-separated values, and the calculator will instantly display the results for both population and sample types.

What is Standard Deviation?

Standard deviation (σ) measures the amount of variation or dispersion in a set of values. A low standard deviation means values are close to the mean, while a high standard deviation indicates values are more spread out.

Features of the Standard Deviation Calculator

Instant Calculation: Results update as you type, no need to press a button.
Population & Sample: Choose between population and sample calculations.
Step-by-Step Solution: See the calculation steps for transparency and learning.
High Precision: Results are shown up to 8 decimal places.
User-Friendly Interface: Clean, modern design for easy use on any device.

How to Use

Enter your data as comma-separated values. Select whether your data represents a population or a sample. The calculator will instantly show the standard deviation and related statistics.

Example:

Input: 12, 15, 18, 20, 22, 25, 28, 30, 32, 35, 40

Count (N): 11
Sum (Σx): 332
Mean (μ): 30.18181818
Variance (σ²): 23.70909091
Standard Deviation (σ): 4.87022447