Standard Deviation Calculator
Calculate standard deviation, variance, mean, and more
What Is Standard Deviation?
Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means numbers are close to the mean, while a high standard deviation means numbers are more spread out. It's a key concept in statistics used in research, finance, and data analysis.
How to Use
- Select data format (List or Frequency)
- Enter your numbers (comma separated)
- Choose Population or Sample calculation
- Click "Calculate" to see your results
Examples
Test Scores
Data: 85, 90, 78, 92, 88, 76, 95
Mean: 86.3
Standard Deviation: 7.2
Variance: 51.8
Frequency Data
Values: 1, 2, 3, 4
Frequencies: 2, 5, 3, 1
Mean: 2.36
Standard Deviation: 0.86
Understanding Your Results
Mean
The average of all values in your dataset.
Variance
The average of squared differences from the mean. It's the square of standard deviation.
Population vs Sample
Population uses all data points (÷ n). Sample uses a subset (÷ n-1) for unbiased estimation.
Sum of Squares
The sum of squared deviations from the mean.
FAQs
What is the difference between population and sample standard deviation?
Population SD divides by n, sample SD divides by n-1 to account for sampling bias.
Why is standard deviation important?
It helps understand data spread and identify outliers. Used in quality control, finance, and scientific research.
What is a good standard deviation?
It depends on your data. Lower SD means more consistent data. Compare to the mean: SD/Mean × 100 = Coefficient of Variation.