Calculate the mean (average), median, mode, and range of any set of numbers instantly.
📖 Standard Descriptive Statistics FormulasFill in the fields on the left with your information, then press Calculate to see your result instantly. No sign-up required, and no data is sent anywhere — everything is calculated right in your browser.
The three measures of central tendency — mean, median, and mode — summarize an entire dataset in a single representative number. The mean is the sum of the values divided by their count, the most commonly used measure but sensitive to extreme outliers. The median is the middle value after sorting the data in ascending order, and is preferred when extreme values exist because it isn't affected by them. The mode is the most frequently occurring value in the dataset, and there may be more than one mode, or no mode at all if every value appears exactly once. This tool calculates all three measures at once, plus the range (the difference between the largest and smallest value) and the count and sum of the values, making it an essential tool for any initial statistical analysis or descriptive statistics homework. Comparing all three side by side is itself informative: a large gap between the mean and median is often the clearest quick signal that a dataset contains outliers skewing the average.
The word 'average' in everyday speech almost always refers to the mean, but statisticians deliberately distinguish between three different measures of central tendency because each one answers a slightly different question, and choosing the wrong one can genuinely mislead.
The mean takes every value in the dataset into account equally, which makes it sensitive to outliers — a single extremely large or small value can shift the mean substantially even if the rest of the data is tightly clustered. This is exactly why average household income figures are often reported alongside the median: a handful of extremely high earners can pull the mean income well above what a 'typical' household actually earns, while the median — the value that sits exactly in the middle of the sorted data — is unaffected by how extreme the highest or lowest values happen to be.
The median's resistance to outliers is precisely why it is the standard choice for reporting figures like home prices, income, and other datasets known to be skewed by a small number of very high (or very low) values. Reporting only the mean home price in a market with a handful of ultra-luxury properties would overstate what a typical buyer should expect to pay.
The mode serves a different purpose entirely — it identifies the single most common value, which matters when the question is about frequency rather than typical size. A clothing retailer deciding how much inventory of each shoe size to stock cares about the mode (the most commonly sold size), not the mean or median size, which might not correspond to any size actually sold in a whole number.
A dataset can have no mode at all (if every value is unique), one mode, or multiple modes tied for the highest frequency — unlike the mean and median, which always produce exactly one value each. Range, meanwhile, is a simple but useful companion statistic: the difference between the highest and lowest values gives a quick sense of how spread out the data is, though it says nothing about how the values are distributed between those two extremes, which is where standard deviation becomes the more informative measure.
The mean is the arithmetic average of all values, while the median is the middle value when data is sorted — the median is less affected by extreme outliers.
Yes, this is called 'multimodal' data, and the calculator lists all values that share the highest frequency.
Then there is no mode, since no value repeats more than any other.