Standard Deviation Calculator
Results:
What is Standard Deviation Calculator?
Standard deviation measures how spread out data points are from the mean (average). It's calculated using the formula σ = √(Σ(x-μ)²/n) for population or s = √(Σ(x-x̄)²/(n-1)) for sample data.
A low standard deviation means data points are close to the mean, while a high standard deviation indicates data is more spread out. This calculator handles both population and sample standard deviation calculations.
How It Works
Enter Data
Input comma-separated values
Calculate σ/s
Get standard deviation
Common Examples
Test Scores
Data: 85, 90, 78, 92, 88
- Mean: 86.6
- Population σ: 4.97
- Sample s: 5.55
Heights (cm)
Data: 170, 175, 168, 180, 172
- Mean: 173
- Population σ: 4.24
- Sample s: 4.74
Sales Data
Data: 100, 120, 95, 110, 105
- Mean: 106
- Population σ: 8.72
- Sample s: 9.75
Standard Deviation Comparison
| Data Set | Mean | Population σ | Sample s |
|---|---|---|---|
| 1, 2, 3, 4, 5 | 3.0 | 1.414 | 1.581 |
| 10, 20, 30 | 20.0 | 8.165 | 10.0 |
| 5, 5, 5, 5 | 5.0 | 0.0 | 0.0 |
| 1, 10, 100 | 37.0 | 41.633 | 50.991 |
| 2, 4, 6, 8 | 5.0 | 2.236 | 2.582 |
Frequently Asked Questions
What's the difference between population and sample standard deviation?
Population (σ) divides by n, while sample (s) divides by n-1. Use population when you have all data points, sample when working with a subset.
What does a high standard deviation mean?
A high standard deviation indicates data points are spread far from the mean, showing high variability in the dataset.
Can standard deviation be negative?
No, standard deviation is always non-negative since it's the square root of variance (which is always positive or zero).
What's the relationship between variance and standard deviation?
Standard deviation is the square root of variance. Variance is in squared units, while standard deviation is in the same units as the original data.
How do I interpret standard deviation values?
In a normal distribution, about 68% of data falls within 1σ, 95% within 2σ, and 99.7% within 3σ of the mean.