Standard Deviation & Statistics Calculator
Paste a list separated by commas, spaces or new lines and get sample and population standard deviation, variance, mean, median, mode, quartiles, outliers and z-scores, worked step by step.
Free · No sign-upHow to use Standard Deviation Calculator
- 1. Paste or type your numbers. Commas, spaces, tabs, semicolons and new lines all work, so you can paste a column straight from Excel or Google Sheets.
- 2. Choose Sample (divide by n − 1) if the numbers are a subset of a bigger group, or Population (divide by n) if they are the whole group.
- 3. Read the results: standard deviation, variance, mean, median, mode, range, quartiles, IQR and any outliers, plus a box plot.
- 4. Open Step by step to see every calculation, check the z-score of each value, then copy the results, download the z-scores as CSV or share a link.
Frequently asked questions
What is the difference between sample and population standard deviation?
Population standard deviation (σ) divides the sum of squared deviations by N and is used when you have every member of the group. Sample standard deviation (s) divides by n − 1 and is used when your data is a sample from a bigger group; it corrects the tendency of a sample to underestimate the spread. For 2, 4, 4, 4, 5, 5, 7, 9 the population SD is 2 and the sample SD is about 2.138.
How do you calculate standard deviation by hand?
Find the mean, subtract it from each value and square the result, add up those squares, divide by n − 1 (sample) or n (population) to get the variance, then take the square root. The Step by step panel shows each of these numbers for your data.
Why are my quartiles different from Excel or my calculator?
There are several accepted ways to compute quartiles. The default here, median of halves, matches the TI-84 and most statistics textbooks. Choose Excel QUARTILE.INC or QUARTILE.EXC to match a spreadsheet. The methods agree on large data sets but can differ on small ones.
How are outliers found?
With Tukey’s fences: any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged, where IQR = Q3 − Q1. Outliers are shown in red in the z-score table and as open circles on the box plot.
What does a z-score tell me?
How many standard deviations a value is from the mean: z = (x − mean) ÷ SD. A z-score of 2 means the value is two standard deviations above average; values beyond about ±2 or ±3 are unusual.
What formats can I paste?
Numbers separated by commas, spaces, tabs, semicolons, pipes or line breaks, including negatives, decimals and scientific notation like 1.2e3. If your numbers use a comma as the decimal mark (1234,5), switch the decimal mark setting. Anything that isn’t a number is ignored and listed so you can check it.