Statistics Calculator

Descriptive statistics summarize a dataset using a few representative numbers. The three classic measures of central tendency — mean, median and mode — each describe the "middle" of the data in a different way. Mean is the arithmetic average, median is the middle value when the data is sorted, and mode is the most frequently occurring value.

Mean is sensitive to outliers; one extremely large value can pull it in that direction. Median is robust to outliers, which is why income statistics often report median rather than mean income. Mode works for both numeric and categorical data and is the only useful measure of central tendency for purely categorical variables.

Standard deviation measures spread — how far values typically lie from the mean. A small standard deviation means the data clusters tightly around the mean; a large one means it spreads widely. For normally distributed data, about 68% of values lie within one standard deviation of the mean, and about 95% within two.

The frequency chart shows how often each value appears, giving a quick visual sense of the distribution shape: symmetric, skewed, uniform, bimodal and so on. Use this calculator for homework, data exploration or any quick analysis that does not require a full spreadsheet.

Variance and standard deviation are closely related — variance is the average of squared deviations from the mean, and standard deviation is the square root of variance. Squaring the deviations before averaging punishes large deviations more than small ones and conveniently removes negative signs. Taking the square root at the end returns the result to the original units of the data, which makes standard deviation more interpretable than variance for most everyday purposes.

Sample versus population statistics is an important distinction. When your data represents the entire population (every student in your class, every transaction in a closed dataset), divide by n. When it represents a sample drawn from a larger population (10 students out of a school of 1,000), divide by n − 1 instead — this is Bessel's correction, and it gives an unbiased estimate of the population variance. Most introductory statistics courses use n − 1, and so do most spreadsheet programs by default.

Quartiles, percentiles and the interquartile range (IQR) extend the idea of the median to give you a richer picture of the distribution. The IQR (Q3 − Q1) is a robust measure of spread that ignores outliers, and the 1.5 × IQR rule is the standard heuristic for flagging outliers in a boxplot. Even when this calculator only reports the basics, knowing what the next layer of descriptive statistics looks like prepares you for more advanced data analysis tools.

Be careful about how you summarise data. Reporting only the mean of skewed data is misleading — house prices, incomes and city populations are almost always right-skewed, which is why the median is the more honest summary. When the mean and median diverge, that is a signal that the distribution is asymmetric and that further investigation is warranted. A simple histogram or boxplot often tells you more than any single number can.