Mean Median Mode Range Calculator

Each one is sensitive to different things. The mean uses every value, so a single outlier drags it; the median only cares about position, so it sits where half the data falls below; and the mode only counts frequency, so it pins the most common value regardless of where it sits. For [1, 2, 3, 4, 100] the mean is 22, the median is 3, and there is no mode. If your three numbers disagree by a lot, you almost always have skew or an outlier, and the median is the safer summary.

Report the range when you actually care about the extremes (worst-case latency, hottest day, biggest order) because it tells you the full spread from min to max. Report the IQR (Q3 minus Q1) when you want a typical spread that ignores extreme values: it covers the middle 50% of the data and barely moves when a single outlier joins or leaves the dataset. The range is fragile; the IQR is robust. Pair the median with the IQR and the mean with the standard deviation.

Use sample variance (divisor n - 1, called Bessel's correction) when your numbers are a sample drawn from a larger population you are trying to estimate, which is the usual case. Use population variance (divisor n) only when your numbers literally are the entire population, for example every student in a single class when no inference beyond that class is intended. Dividing by n - 1 instead of n corrects for the bias that sample mean fits the sample slightly better than it fits the underlying population. The calculator shows both numbers so you can pick the right one without re-entering your data.

It uses the simplest classical rule: compare the mean and the median. If the mean is meaningfully larger than the median the data is skewed right (long right tail), if it is meaningfully smaller the data is skewed left (long left tail), and if they are close the data is roughly symmetric. The tolerance is scaled to the IQR so floating-point noise in symmetric datasets is not mislabelled. This is a quick verdict, not a formal skewness coefficient: if you need Pearson or Fisher skewness as a number, run the data through a dedicated skewness tool.

For a single number that summarizes a typical value: mean if the data is symmetric and outlier-free, median if it is skewed or has outliers, mode if you care about the most common category (especially for discrete data like shirt sizes). For spread: standard deviation pairs with the mean, IQR pairs with the median, and range is for headline extremes. Quartiles and IQR also drive boxplots and Tukey's 1.5 x IQR outlier rule, which is why this calculator shows them alongside the centers and the simpler range.