Standard Deviation Calculator
Calculate standard deviation to measure data spread and variability.
Enter Numbers (comma-separated)
Variance: 62.5
Mean: 15
Calculation:
1. Mean = 15
2. Squared differences: (5-15)²=100, (10-15)²=25, (15-15)²=0, (20-15)²=25, (25-15)²=100
3. Sum of squared differences = 250
4. Variance = 250 / 4 = 62.5
5. Standard Deviation = √62.5 = 7.91
What is Standard Deviation?
Standard deviation measures how spread out numbers are from their mean.
Sample Standard Deviation: s = √[Σ(x - x̄)² / (n - 1)]
Population Standard Deviation: σ = √[Σ(x - μ)² / n]
- Low standard deviation = data points close to mean
- High standard deviation = data points spread out
How to Calculate Standard Deviation
- Find the mean (average) of all values
- Find each deviation from the mean: (value - mean)
- Square each deviation: (value - mean)²
- Sum all squared deviations
- Divide by n-1 (sample) or n (population)
- Take the square root to get standard deviation
Sample vs. Population
- Sample: Use when analyzing a subset of data (divide by n-1)
- Population: Use when you have all the data (divide by n)
Most of the time, you'll use sample standard deviation.
Why It Matters
Standard deviation tells you: - How consistent your data is - How much variation exists - Whether data points are clustered or spread out - The reliability of the mean
Common Questions
What is standard deviation?
Standard deviation measures how spread out numbers are from their mean. Low values mean data is close to the mean; high values mean data is spread out.
What is the difference between sample and population standard deviation?
Sample standard deviation divides by (n-1) and is used for sample data. Population standard deviation divides by n and is used when you have the entire population.