Descriptive Statistics Calculator
Enter a numeric dataset to compute summary statistics, distribution shape measures, and a histogram. Values can be comma or newline-separated.
Central Tendency
Spread
Range & Quartiles
Shape
Frequently asked questions
When should I use the mean versus the median?
Use the mean when your data are roughly symmetric and have no extreme outliers. The mean uses every value, so a single very large or very small number shifts it considerably. The median is the middle value after sorting, so outliers have no special power over it. For skewed distributions like income, house prices, and wait times, the median is usually more representative. When both are reported, comparing them is itself informative: a mean much larger than the median signals right skew.
What is the difference between sample and population standard deviation?
Population SD (σ) divides by n and is correct when your data are the entire population. Sample SD (s) divides by n − 1 (Bessel's correction) and is the right choice when your data are a sample drawn from a larger population and you want an unbiased estimate of that population's spread. In practice, n − 1 matters most for small samples; for n > 30 the difference is negligible.
How do I interpret skewness?
Skewness measures asymmetry around the mean. A value near 0 is roughly symmetric. Positive skewness means a longer right tail (most values cluster on the left with a few large outliers pulling the mean up). Negative skewness is the mirror: a long left tail. The calculator uses the Fisher-Pearson adjusted coefficient, which corrects for sample size. Values beyond ±1 are generally considered substantially skewed; beyond ±2, markedly so.
What does excess kurtosis tell me?
Kurtosis describes tail heaviness relative to a normal distribution. Excess kurtosis subtracts 3 so that a normal distribution scores 0. Positive excess kurtosis (leptokurtic) means heavier tails and a sharper peak. Outliers are more likely than a normal distribution would predict. Negative excess kurtosis (platykurtic) means lighter tails and a flatter peak. Kurtosis is sensitive to extreme values and is only reliable for reasonably large samples (n > 20 as a rough guide).
What is the IQR and why is it useful?
The interquartile range is Q3 − Q1: the spread of the middle 50% of your data. Because it ignores the outer quarters entirely, it is resistant to outliers. The IQR is the basis for box plots and the common outlier fence rule: values more than 1.5 × IQR below Q1 or above Q3 are flagged as potential outliers (3 × IQR for "extreme" outliers). When comparing spread across groups, the IQR is more informative than the full range whenever outliers or skew are present.