Welcome to the Standard Deviation Calculator. The Standard Deviation Calculator helps you measure how spread out the numbers are from their average (mean). It is commonly used in statistics, mathematics, finance, and research to understand data variability.
If the standard deviation is low, the numbers are close to the average.
If the standard deviation is high, the numbers are more spread out.
Standard Deviation Calculator
Enter numbers separated by commas to calculate mean and standard deviation instantly.
What is Standard Deviation?
Standard deviation is a statistical measure that shows how much variation exists in a dataset. It tells us how far each number is from the mean (average).
Why is it Important?
Standard deviation is useful for:
- Analyzing exam results
- Measuring investment risk
- Scientific research
- Business data analysis
- Quality control
Formula Used
Population Standard Deviation Formula:
σ = √[ Σ (x − μ)² / N ]
Where:
- x = Each value
- μ = Mean (Average)
- N = Total number of values
Example
For numbers: 2, 4, 6, 8
- Mean = (2 + 4 + 6 + 8) ÷ 4 = 5
- Differences = -3, -1, 1, 3
- Squares = 9, 1, 1, 9
- Average of squares = 5
- Square root of 5 = 2.236
Standard deviation = 2.236