Enter your data as comma-separated values and instantly get the mean, median, mode, variance and standard deviation.
Mean, Median, Mode & Standard Deviation Calculator
How It’s Calculated
Mean is the sum divided by the count. Median is the middle value once sorted — the average of the two middle values if n is even. Mode is the most frequently occurring value. Variance averages the squared distance of every value from the mean, and standard deviation is its square root — back in the original units. This tool shows both the population version (divide by n) and the sample version (divide by n−1), since PUC and VTU questions use both depending on context.
Worked Example
For {4,8,6,5,3,8,9}: n=7, mean = 43/7 ≈ 6.14, sorted data is {3,4,5,6,8,8,9} so median = 6, mode = 8 (appears twice).
Frequently Asked Questions
Q: When do I use population vs sample standard deviation?
Use the population formula (÷n) when your data is the entire group you care about. Use the sample formula (÷(n−1)) when your data is a sample used to estimate a larger population — 2nd PUC mostly uses the population version unless a question specifies otherwise.
Q: What if every value appears exactly once?
There’s no mode — this calculator will tell you that directly rather than listing every value.
Statistics is one of the more mechanical, learnable chapters in 1st PUC — the formulas don’t change, only the data. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →