Statistics Calculator: Mean, Median, Mode & Std Dev
Paste a list of numbers and instantly get the mean, median, mode, range, variance, and standard deviation, both population and sample.
How This Statistics Calculator Works
Descriptive statistics summarize a data set with a handful of representative numbers instead of forcing you to look at every individual value. The three most common measures of central tendency, mean, median, and mode, each describe a data set’s ‘typical’ value in a different way: the mean is the arithmetic average, the median is the middle value when everything is sorted, and the mode is the most frequently occurring value.
Variance and standard deviation measure spread, how far individual values tend to be from the mean. This tool calculates both the population version (dividing by N, used when your data represents an entire group you care about) and the sample version (dividing by N−1, used when your data is a subset drawn to estimate a larger population), since using the wrong one is a common source of subtly incorrect results, especially the sample version’s N−1 divisor, known as Bessel’s correction, which adjusts for the fact that a sample’s variance tends to slightly underestimate the true population variance.
Simply paste in your numbers, separated by commas, spaces, or line breaks, in any combination, and every statistic is calculated and displayed instantly, entirely within your browser.
What this tool does
How to use it
Paste your data
Enter your numbers separated by commas, spaces, or line breaks, or click Load Sample Data to see an example.
Click Calculate Statistics
Every measure is computed instantly from your data set.
Review central tendency and spread
Check the mean, median, and mode for a ‘typical’ value, and the variance/standard deviation for how spread out your data is.
Choose population vs. sample
Use the guidance shown to pick whichever variance and standard deviation figures match your actual data context.
FAQ: Statistics Calculator
The mean is the sum of all values divided by how many there are (the arithmetic average). The median is the middle value when the data is sorted (or the average of the two middle values if there’s an even count), which is less affected by extreme outliers than the mean. The mode is the value that appears most frequently, and a data set can have one mode, multiple modes (multimodal), or no mode at all if every value is unique.
Use the median when your data contains outliers or is heavily skewed, since a few extreme values can pull the mean far from what feels ‘typical,’ while the median stays anchored to the actual middle of the sorted data. A classic example is household income, where a small number of very high earners inflate the mean well above what most households actually earn, making the median a more representative figure.
Population standard deviation divides the sum of squared differences by N (the total count) and is used when your data represents every member of the group you’re studying. Sample standard deviation divides by N−1 instead, a correction (called Bessel’s correction) that compensates for the tendency of a sample to underestimate the true variability of the full population it was drawn from. Since most real-world data collection involves sampling rather than measuring an entire population, the sample version is more commonly the correct choice.
When you calculate variance using a sample’s own mean (rather than the true population mean, which is usually unknown), the result systematically underestimates the true population variance, because the sample mean is, by definition, the value that minimizes the sum of squared distances within that particular sample. Dividing by N−1 instead of N corrects for this bias, producing a more accurate estimate of the population’s actual variance.
A large standard deviation means your data points are spread out widely around the mean, indicating high variability, while a small standard deviation means values cluster tightly around the mean. For example, two classes could have the same average test score, but one with a small standard deviation had most students scoring close to that average, while one with a large standard deviation had scores spread from very low to very high.
If every value in your data set appears exactly once, there’s no value that occurs more often than any other, so the data set has no mode, this is a normal and valid outcome, not an error. This is especially common in continuous, precisely measured data (like exact temperatures or prices) where exact repeated values are less likely than in categorical or rounded data.