How to use
- 1Paste or type your numbers, separated by commas, spaces, semicolons or new lines.
- 2Check the counter: it shows how many values were read and lists anything skipped.
- 3Read the mean, median and both standard deviations at the top.
- 4Scroll down for variance, quartiles, IQR, coefficient of variation, the histogram and the sorted data.
Sample vs. population standard deviation
Standard deviation measures how spread out values are around the mean. The population SD (σ) divides the sum of squared deviations by n and is correct when your data covers every member of the group. The sample SD (s) divides by n − 1 (Bessel’s correction) and is the right choice when your numbers are a sample used to estimate a larger population — which is most real-world cases. For the example data 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, σ = 2 and s ≈ 2.138. In Excel and Google Sheets these are STDEV.P and STDEV.S.
Median, mode and quartiles
The median is the middle value of the sorted data, or the average of the two middle values when n is even. The mode is the most frequent value; tied values are all listed, and if every value occurs equally often there is no mode. Quartiles use linear interpolation, the same method as Excel’s QUARTILE.INC: Q1 is the 25th percentile, Q3 the 75th, and the interquartile range IQR = Q3 − Q1 spans the middle half of the data. A common rule flags values more than 1.5 × IQR beyond the quartiles as potential outliers.
Coefficient of variation and histogram
The coefficient of variation (CV) is the sample SD divided by the absolute value of the mean, shown as a percentage, so you can compare variability between data sets on different scales. The histogram groups values into bins using Sturges’ rule (⌈log₂ n⌉ + 1 bins, at most 30); hover over a bar to see its range and count. Everything runs in your browser, so you can paste a column straight from a spreadsheet.
Frequently asked questions
Should I use sample or population standard deviation?
Use the sample SD (s) if your data is a subset — survey answers, one class’s test scores, measurements from a batch. Use the population SD (σ) only if you have data for the entire group you are describing.
How is standard deviation calculated?
Find the mean, subtract it from each value and square the result, add up those squares, divide by n (population) or n − 1 (sample), then take the square root.
What is the difference between variance and standard deviation?
Variance is the average squared deviation from the mean; the standard deviation is its square root, which puts it back into the same units as the data.
Can I paste numbers from Excel?
Yes. Copy a column and paste it — values on separate lines or separated by tabs are read automatically. Non-numeric entries such as headers are skipped and listed.
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