Standard Deviation Calculator
Standard Deviation Calculator
How it works: This calculator calculates comprehensive statistics for your data set, including standard deviation, variance, mean, median, mode, and more. Enter numbers separated by spaces, commas, or semicolons. Choose between sample standard deviation (n-1 denominator) for sample data or population standard deviation (n denominator) for complete populations. Standard deviation measures how spread out the data is from the mean.
Overview
Comprehensive statistics calculator that calculates standard deviation, variance, mean, median, mode, range, sum, and count for data sets. Features include sample and population calculations, complete statistical analysis, and step-by-step formulas.
About
Understanding Statistical Measures
Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. It's one of the most important measures in statistics and data analysis.
Features:
- Sample and population standard deviation
- Complete statistical analysis
- Mean, median, and mode calculations
- Variance and range calculations
- Step-by-step formulas and explanations
Sample vs Population
Sample standard deviation uses n-1 in the denominator and is used when you have a subset of data and want to estimate the population parameter. Population standard deviation uses n and is used when you have all possible data points. The choice affects the result and interpretation of the analysis.
FAQ
What's the difference between sample and population standard deviation?
Sample uses n-1 denominator (unbiased estimate for samples). Population uses n denominator (actual for complete data).
What does standard deviation measure?
It measures how spread out data is from the mean. Low SD = data clustered close to mean. High SD = data spread out.
How do you calculate variance?
Variance is the square of standard deviation. It's calculated as the average of squared differences from the mean.
What's a normal distribution?
In a normal distribution, about 68% of data falls within 1 SD of mean, 95% within 2 SD, and 99.7% within 3 SD.
When should I use sample vs population?
Use sample when you have a subset of data and want to estimate the population parameter. Use population when you have all possible data.