Standard Deviation & Variance Calculator
with step-by-step working
Calculate mean, variance and standard deviation for any data set instantly ā population or sample ā with every calculation step shown. Free, unlimited, no sign-up needed.
Enter your data set
Standard Deviation & Variance Formulas
Free Online Standard Deviation & Variance Calculator for Indian Students
This free standard deviation and variance calculator instantly computes the mean, variance and standard deviation of any data set ā with the full step-by-step working shown, not just the final number. It's built for TN Board, CBSE, Class 11ā12 and TNPSC Statistics students who need a fast, reliable way to check their homework or exam practice.
Unlike a plain scientific calculator, this tool shows every deviation, (x ā mean)Ā², and the running calculation, so you can see exactly where a formula comes from instead of only getting a final answer. Switch between the population formula (Ć·N) and the sample formula (Ć·Nā1) depending on whether your data represents an entire population or a sample drawn from a larger group ā a distinction that's frequently tested in board exams.
If you're stuck on why the formula works ā not just what the number is ā StudyHelpAI's free AI Statistics tutor explains variance, standard deviation and related concepts step by step in English or Tamil.
ā Back to Statistics Homework HelpStandard Deviation & Variance Calculator ā Questions Answered
Yes ā it's completely free with no sign-up, no daily limit, and no ads. It runs entirely in your browser, so results are instant.
Population standard deviation (Ļ) is used when your data covers an entire group and divides by N. Sample standard deviation (s) is used when your data is a subset used to estimate a larger population, and divides by Nā1 instead ā this correction (called Bessel's correction) accounts for the extra uncertainty in using a sample.
Variance is the average of the squared deviations from the mean. Standard deviation is simply the square root of variance, which brings the value back into the same units as your original data, making it easier to interpret.
Yes ā enter any real numbers separated by commas or spaces, including negative values and decimals, and the calculator will process them correctly.
No ā most board and entrance exams don't allow calculators or phones for statistics questions. Use this tool for practice and homework, but make sure you can reproduce the step-by-step method by hand for exam day, since marks are given for showing your working.