Basic Statistics Calculator
Enter a list of numbers and instantly get mean, median, mode, range, variance, and standard deviation.
I use this for quick data checks, a set of survey scores, attendance numbers over several weeks, anything where I need to understand the shape of the data before presenting it. The standard deviation is the number that tells you whether the data is tightly clustered or widely spread, which changes how you interpret the mean.
The mean tells you the center. The standard deviation tells you how spread out the data is around that center. A mean of 85 means something very different with a standard deviation of 2 vs a standard deviation of 20.
Mean, median, and mode
The mean (arithmetic average) is the sum of all values divided by the count. It's sensitive to outliers, one extreme value can pull the mean significantly. The median is the middle value when data is sorted, it's resistant to outliers and better represents the "typical" value when the distribution is skewed. The mode is the most frequently occurring value, useful for categorical or discrete data where repetition is meaningful. For a perfectly symmetric distribution, mean and median are identical.
Standard deviation and variance
Variance is the average of squared deviations from the mean. Standard deviation is the square root of variance, it restores the original units, making it interpretable in the same scale as the data. A standard deviation of 5 on a dataset of test scores means most scores fall within 5 points of the mean in either direction. The 68-95-99.7 rule for normal distributions: roughly 68% of data falls within 1 standard deviation, 95% within 2, and 99.7% within 3.
Population vs sample standard deviation
This calculator uses population standard deviation (σ), dividing by n. Sample standard deviation (s) divides by n−1 and is used when your data is a sample from a larger population and you're estimating the population's variability. For small samples (under 30), the distinction matters meaningfully. For large datasets, the difference is negligible. If you're analyzing a complete dataset (all scores on a test, all weeks of giving data), population standard deviation is correct.
When the mean lies
The mean can misrepresent a dataset when the distribution is heavily skewed. Income is the classic example, US median household income is about $75,000, but mean household income is significantly higher because a small number of very high earners pull the average up. When reporting central tendency for skewed data, the median is usually more representative of the typical value. Compare mean and median: if they're close, the data is fairly symmetric; if they diverge significantly, skew is present.
Frequently asked questions
What if my data has no mode?
If no value appears more than once, there is no mode, or equivalently, every value is equally "the mode." In practice, mode is most useful for discrete data (test scores, survey ratings) where values repeat. For continuous data (precise measurements), mode is rarely meaningful.
What does a high standard deviation tell me?
High standard deviation means data points are spread widely around the mean, high variability. Low standard deviation means they're clustered tightly. In business contexts: low variance in customer satisfaction scores is good (consistently positive). Low variance in product dimensions is good (quality control). High variance in either case signals inconsistency worth investigating.
How many data points do I need for meaningful statistics?
There's no universal minimum, but general guidance: for a mean and standard deviation to be reliable, at least 30 data points is a common threshold. The central limit theorem, which underlies most statistical inference, begins to hold reliably around n=30. For smaller samples, interpret statistics with appropriate caution about generalizability.