Calculate standard deviation, variance, and other statistical measures.
Standard Deviation
7.21
Variance
52.00
Mean (Average)
23.70
Additional Statistics
Count
10
Sum
237
Minimum
12
Maximum
35
Range
23
Median
23.5
Your Data Values (sorted):
Data Visualization
📐 Formulas Used
Population Standard Deviation (σ):
σ = √[Σ(x - μ)² / N]
Sample Standard Deviation (s):
s = √[Σ(x - x̄)² / (n - 1)]
Where:
• x = each value
• μ or x̄ = mean
• N or n = number of values
• Σ = sum of
σ = √[Σ(x - μ)² / N]
Sample Standard Deviation (s):
s = √[Σ(x - x̄)² / (n - 1)]
Where:
• x = each value
• μ or x̄ = mean
• N or n = number of values
• Σ = sum of
💡 What is Standard Deviation?
Standard deviation measures how spread out numbers are from their average. A low standard deviation means values are close to the mean, while a high standard deviation means they're more spread out.
Standard deviation measures how spread out numbers are from their average. A low standard deviation means values are close to the mean, while a high standard deviation means they're more spread out.
🎓 Population vs Sample:
- Population (σ): Use when you have data for the entire group you're studying
- Sample (s): Use when you have data from a subset of a larger group
- Sample standard deviation divides by (n-1) instead of n, which gives a better estimate
📝 Tips:
- Enter numbers separated by commas, spaces, or line breaks
- Decimal numbers are supported (e.g., 12.5, 18.7)
- The calculator will automatically sort and clean your data
- Variance is the square of standard deviation (σ² or s²)