Standard Deviation Calculator
Calculate the standard deviation (sample and population) of any dataset. The most widely used measure of data spread, shown with variance, mean, and full statistics.
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š How to Use
Step 1: Enter your numbers separated by commas or spaces. Click "Example" for a demo dataset.
Step 2: Click "Calculate" for instant results with box plot and interpretation.
Step 3: Use "Copy" or "CSV" to export results. Click "Recalculate" to try new data.
What Is Standard Deviation?
Standard deviation (SD) measures the average distance of data points from the mean. A low SD indicates data clustered near the mean; a high SD indicates widely spread data. It is the square root of the variance and is expressed in the same units as the data.
Sample vs Population Standard Deviation
Population SD (Ļ) = ā(Ī£(xāĪ¼)Ā² / N). Sample SD (s) = ā(Ī£(xāxĢ)Ā² / (Nā1)). Most real-world data is a sample, so sample SD is the default in this calculator.
The 68-95-99.7 Rule
For normally distributed data: about 68% of values fall within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD. This empirical rule helps interpret what a given standard deviation means in practical terms.
ā Frequently Asked Questions
What is a good standard deviation?
It depends entirely on context. A SD of 5 is huge for exam scores out of 10, but tiny for stock prices in hundreds. Compare SD to the mean using the coefficient of variation (CV = SD/Mean Ć 100%).
How is SD different from IQR?
SD uses all data points and is sensitive to outliers. IQR uses only Q1 and Q3 and is robust to outliers. For non-normal data, IQR is often more informative.
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