Mean, Median, Mode Calculator

Mean, median, and mode are the three familiar measures of central tendency. Each condenses a collection of observations into a representative value, but each defines the center differently. Seeing them together helps reveal whether a distribution is balanced, skewed, concentrated, or affected by unusual observations. This calculator also reports range, population variance, and population standard deviation so that center and spread can be interpreted side by side. The arithmetic mean is the sum of all values divided by their count. Every observation contributes to it, which makes the mean mathematically useful but sensitive to outliers. One exceptionally high house price, salary, or response time can pull the mean upward. The median is the middle value after sorting. If the number of observations is even, it is the average of the two middle values. Because only position determines the median, extreme values have much less influence on it. The mode is the value that appears most often. A data set can have one mode, several modes tied for the highest frequency, or no mode when every value occurs equally often. Unlike the mean, the mode must be an observed value. It is especially useful for discrete counts and categories, although this calculator works with numeric observations. When two or more values share the highest repeated frequency, every tied value is displayed. Comparing the three measures gives useful context. In a roughly symmetric, single-peaked distribution, the mean, median, and mode tend to be close. In a right-skewed distribution, high outliers commonly make the mean larger than the median. In a left-skewed distribution, low outliers commonly make it smaller. A mode far from the mean and median can indicate clusters or repeated values that deserve closer inspection. Range is the maximum minus the minimum and provides the quickest measure of total spread. Population variance averages the squared distances from the mean, and population standard deviation is its square root. Squaring prevents positive and negative differences from canceling and emphasizes larger deviations. This tool treats the entered values as a complete population and divides variance by n. A sample variance intended to estimate a larger population would instead divide by n − 1. Enter integers, decimals, or negative values using commas, spaces, or both. The tool sorts a copy of the data for the median without changing the values used for the other calculations. Use these results as a compact descriptive summary, then consider a chart or a more detailed statistical method whenever distribution shape, sampling design, or inference matters.