Standard Deviation Calculator
Calculate Variance, Mean & Statistical Measures
Professional statistics calculator for standard deviation, variance, and descriptive statistics. Supports both sample and population calculations with step-by-step solutions.
Used by researchers
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Accurate calculations
Standard Deviation Calculator
Calculate standard deviation, variance, and statistical measures for your dataset
Use for sample data (most common) - unbiased estimator using n-1
Parsed values: 2, 4, 4, 4, 5, 5, 7, 9
Sample Datasets
Statistical Results
Standard deviation, variance, and descriptive statistics
Enter valid data values to see the statistical analysis
Understanding Standard Deviation
Learn how standard deviation measures data spread and variability.
What is Standard Deviation?
Standard deviation measures how spread out numbers are from their average. A low SD means data points cluster near the mean; high SD means they're more spread out.
Sample vs Population
Sample SD uses n-1 (Bessel's correction) for unbiased estimation. Population SD uses n when you have the complete dataset.
Variance
Variance is the square of standard deviation. SD = sqrt(variance). Variance is in squared units, SD is in original units.
The 68-95-99.7 Rule
For normal distributions: 68% of data falls within 1 SD, 95% within 2 SD, and 99.7% within 3 SD of the mean.
Coefficient of Variation
CV = (SD / Mean) x 100%. Allows comparison of variability between datasets with different units or scales.
Practical Applications
Used in quality control, finance (risk assessment), science (measurement uncertainty), and social sciences (data analysis).
Key Statistical Measures
Mean (Average)
- Sum of all values / count
- Central tendency measure
- Affected by outliers
- Symbol: x-bar or mu
Median
- Middle value when sorted
- Not affected by outliers
- Better for skewed data
- 50th percentile
Range
- Max value - Min value
- Simplest spread measure
- Sensitive to outliers
- Quick overview of spread
IQR
- Q3 - Q1 (middle 50%)
- Robust to outliers
- Used in box plots
- Interquartile Range
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