Use this mean and median calculator to find the average, median, mode, and range of any list of numbers. Supports decimals, negatives, and custom delimiters, with a step-by-step breakdown and adjustable rounding precision.
Use template ->What is the mean?
The arithmetic mean is the sum of all values divided by how many there are. It is what most people refer to as “the average” and gives a sense of the central level of a dataset. Its main limitation is sensitivity to outliers: a single extreme value can pull the mean far from where most of the data actually sits.
The median is the middle value when data is sorted in order. For an even number of values, it is the average of the two middle ones. Because it depends only on rank rather than magnitude, it is unaffected by extreme values and often gives a more representative picture of center when the data is skewed.
Mean and median formulas
Mean: x̄ = (1/n) × Σxᵢ
Where x̄ is the arithmetic mean, n is the count of values, xᵢ represents each individual value, and Σ denotes summation across all values.
Median: the value at position (n+1)/2 when sorted ascending. For an even-count dataset, it is the average of the values at positions n/2 and (n/2)+1.
How the mean and median calculator works
The calculator parses a list of numbers with automatic delimiter detection and returns count, sum, mean, median, mode, and range together. The step-by-step breakdown shows n, Σxᵢ, and the final division, which makes the arithmetic traceable rather than just asserted.
Mode is included because it captures the most frequent value, which is a different kind of central tendency question from mean or median. Range (min to max) gives a quick read on spread without requiring a full variance calculation. Rounding precision is adjustable so outputs can match the reporting context.
How mean and median are used in practice
Mean and median appear in almost every context where a dataset needs to be summarised: financial reporting, performance analytics, scientific measurement, and operational review. The choice between them is rarely arbitrary. Mean works well when data is roughly symmetric and outliers are not a concern. Median is preferred when distributions are skewed or when a single atypical value should not distort the summary.
In salary analysis, for instance, median compensation is nearly always more informative than mean, because a small number of very high earners pull the mean upward without reflecting what most people actually earn. The same logic applies in housing prices, customer order values, and any domain where the distribution has a long tail.