Mean / Median / Mode Calculator

For a data set: mean is the arithmetic average (sum divided by count); median is the middle value when sorted (or the average of the two middle values for even counts); mode is the most frequent value or values; range is the difference between maximum and minimum.

Enter comma- or whitespace-separated numbers to see all four. The mean reflects every value but is sensitive to outliers; the median is robust; the mode reveals concentration but doesn't exist for fully unique sets; the range gives a quick spread but ignores distribution shape.

The definitions are first-day-of-statistics material, but their behaviors diverge in informative ways. Mean is influenced by every value — a single outlier can pull it dramatically. Median is robust: any single value beyond the middle position can be moved arbitrarily far without affecting the median at all. Mode requires repeated values to exist; for fully unique data, the mode is undefined or technically every value (each appearing once). For a normal distribution, all three coincide at the center. For a skewed distribution, they spread out: mean follows the tail, median sits at the middle of the count, mode marks the peak frequency. The order in which they appear (left-skew has mean < median < mode; right-skew is the reverse) is the standard interpretation rule.

A worked example. The data set [12, 15, 16, 18, 19, 20, 22, 24, 28, 95]. Mean = 269/10 = 26.9. Median = (19 + 20)/2 = 19.5. Mode = no repeats, undefined (or all values, depending on convention). Range = 95 - 12 = 83. The 95 is clearly an outlier. Mean of 26.9 is dragged 7 points above the median by that single value. The median better represents the 'typical' value here. Reporting just the mean would mislead anyone trying to understand where most of the data lives. Reporting both — and noting the gap as evidence of skew or outliers — gives a much more honest summary.

Limitations and when each measure misleads. For symmetric distributions, all three are roughly equal and the mean is the most informationally dense (uses all values). For skewed data (incomes, response times, home prices), median better describes the typical experience while mean better describes the total resource. Mode is only meaningful for categorical or discretized continuous data; for true continuous variables, every value is unique and mode is essentially undefined. Range is a poor spread measure because it depends only on the two most extreme values; standard deviation or interquartile range are more useful descriptors of variability. For small samples (under 10 to 15 observations), all three measures are noisy and confidence intervals matter more than the point estimates. Reporting raw values directly is often clearer at low n.