Enter a list of numbers to get the mean, median, mode, range, variance, and standard deviation all at once.
Paste in a list of numbers — test scores, monthly sales, workout times, whatever you're tracking — and this calculator gives you the handful of statistics people actually reach for when they want to understand a data set at a glance. Mean, median, and mode all try to answer the same basic question ("what's typical here?"), but they answer it in different ways, and picking the wrong one can genuinely mislead you. Range, variance, and standard deviation answer a different question: not what's typical, but how spread out the data actually is around that typical value.
The mean is the one everyone learns first — add everything up, divide by how many numbers there are. It's useful, but it's also the most easily distorted by outliers. If nine people in a room earn $50,000 and one earns $2 million, the mean income in that room is over $200,000, which describes basically nobody accurately. The median sidesteps that problem entirely: line every value up in order and take the middle one (or average the two middle ones if there's an even count). It's far more resistant to extreme values, which is why household income and home prices are almost always reported as medians in the news, not means. The mode is different again — it's simply whichever value shows up most often, and it's the only one of the three that also works sensibly on non-numeric categories, like the most common shoe size sold in a store.
Two data sets can share the exact same mean and still be completely different animals. A class where every student scored between 78 and 82 on a test, and a class where scores ranged from 40 to 100, can both average out to an 80 — but they tell wildly different stories about how the class actually performed. Variance and standard deviation are how you capture that difference numerically. Variance takes each value's distance from the mean, squares it (so negative and positive differences don't cancel out), and averages those squared differences. Standard deviation is just the square root of variance, which brings the number back into the same units as your original data, making it far easier to interpret intuitively — a standard deviation of "4 points" on a test score means something you can actually picture, whereas a variance of "16 points squared" doesn't.
There are technically two versions of variance and standard deviation — population and sample — and they differ by a small correction in the denominator (dividing by n for a population, or n−1 for a sample). This calculator defaults to the sample version, since in almost every real-world situation you're working with a sample of a larger group rather than every single member of that group — a handful of test scores from one class period, not every test ever taken by every student everywhere. The n−1 adjustment (called Bessel's correction) exists specifically to correct for the fact that a sample tends to slightly underestimate the true spread of the full population it was drawn from.
This calculator is meant for exactly that kind of fast, practical check — paste your numbers in, and you'll have the full picture in one pass instead of computing each statistic by hand.