Numbers
Standard Deviation Calculator
A standard deviation calculator takes a list of numbers and returns their mean, variance, and standard deviation — both the population and sample versions — so you can measure how spread out your data is. Paste comma-separated values and it computes everything at once. Students use it to check statistics homework, researchers to summarise a dataset quickly, and anyone analysing scores, measurements, or results to gauge consistency. Standard deviation is the most common measure of spread: a small value means the data clusters tightly around the mean, while a large one means it is widely scattered. The tool shows both the population formula (dividing by n) and the sample formula (dividing by n−1), because which you need depends on whether your numbers are the whole population or a sample. Use it to verify a hand calculation, summarise a small dataset, or understand how the population and sample figures differ.
How to use
- Choose your options above
- Click Generate
- Copy your result
Detailed instructions
- Enter your numbers separated by commas.
- Click Generate to compute the statistics.
- Read the mean, variance, and standard deviation.
- Use the population or sample figure as appropriate.
Use Cases
- •Checking standard deviation homework
- •Summarising the spread of a small dataset
- •Comparing the consistency of two sets of results
- •Computing both population and sample statistics
- •Gauging how scattered scores or measurements are
Tips
- →Use the sample figure (n−1) when your data is a sample.
- →A small standard deviation means tightly clustered data.
- →Compare two datasets' spread using their standard deviations.
- →Check the mean first to sanity-check your input.
FAQ
what does standard deviation tell me
It measures how spread out the numbers are around the mean. A small standard deviation means the values cluster tightly together; a large one means they are widely scattered. It is the most common single measure of variability.
what is the difference between population and sample
Use the population version (dividing by n) when your numbers are the entire group you care about. Use the sample version (dividing by n−1) when they are a sample drawn from a larger population, which corrects a slight bias. The tool shows both.
how do i enter my data
Type or paste your numbers separated by commas or spaces — for example 2, 4, 4, 5, 9. Non-numeric values are ignored, and you need at least two numbers for a meaningful spread.
What is the difference between population and sample standard deviation?
Population standard deviation divides by N and is used when your data is the entire group; sample standard deviation divides by N−1 (Bessel's correction) and is used when your data is a sample meant to estimate a larger population. The calculator shows both — use population for complete data, sample for a subset.
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