Standard Deviation Solver
Quantify the spread of your data. Our advanced calculator provides both sample and population metrics with deep variance analysis.
Dataset Entry
0 values detected
Which one to use?
Use **Sample SD** if your data represents a small group from a larger set. Use **Population SD** if you have data for every single member of the group.
Input a dataset to see deviation analysis.
The Concept
Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low SD indicates values stay close to the mean, while a high SD indicates values are spread out over a wider range.
Calculation Steps
- 1Find the arithmetic mean (average).
- 2Subtract the mean from each value and square the result.
- 3Find the average of these squared differences (Variance).
- 4Take the square root of the variance.
Key Definitions
Variance
The average of the squared differences from the Mean.
Sample (n-1)
Used when the data is a subset of a larger population. Corrects for bias.
Population (n)
Used when every possible data point in the group is included.
68-95-99.7 Rule
In a normal distribution, these percentages of data fall within 1, 2, and 3 standard deviations.
Expert Advice
Standard deviation is the most robust way to calculate **Volatility** in financial markets. Traders use it to determine 'Bollinger Bands' and risk exposure.
"The Bell Curve"
Normal Distribution
Most datasets in nature and social science follow this 'Normal' pattern, where the standard deviation determines how steep or flat the curve appears.