Enter a set of numbers into the Data Set field (comma or space separated) and the Median Calculator finds the middle value of your dataset. You also get the mean, mode, range, count, and a sorted list — everything you need to understand your data's central tendency at a glance.
Median
--
Mean (Average)
--
Mode
--
Range
--
Count (n)
--
Sum
--
Minimum
--
Maximum
--
The median is the middle value of a dataset when all numbers are arranged in ascending order. It represents the point where exactly half the values are below it and half are above it. Unlike the mean, the median is not affected by extremely large or small outliers, making it a better measure of the 'typical' value for skewed datasets.
Sort your numbers from smallest to largest. If the count (n) is odd, the median is the middle number at position (n+1)/2. If the count is even, the median is the average of the two middle numbers at positions n/2 and n/2+1. For example, for the set {4, 5, 6, 7}, the median is (5+6)/2 = 5.5.
The mean (average) is calculated by summing all values and dividing by the count, while the median is simply the middle value. The mean is sensitive to outliers — a few very large or small values can pull it far from the 'typical' value. The median is resistant to outliers, making it more representative for skewed data such as income distributions.
Use the median when your dataset contains outliers or is heavily skewed. For example, reporting the median household income is more informative than the mean because a small number of extremely high earners can inflate the mean significantly. For symmetric, normally distributed data, the mean and median will be close to each other.
The median is commonly denoted by x̃ (x-tilde) in statistics, though you may also see it written as M or Med. In some textbooks it is written as x̄ with a tilde accent to distinguish it from the mean (x̄).
When a dataset has an even number of values, there is no single middle number. Instead, the median is calculated as the average of the two middle values. For example, for the set {0, 1, 1, 18}, the two middle values are 1 and 1, so the median is (1+1)/2 = 1.
All three are measures of central tendency in statistics. The mean is the arithmetic average of all values. The median is the middle value when data is sorted. The mode is the value that appears most frequently. Each measure describes what is 'typical' in a dataset in a slightly different way, and the best choice depends on the shape and nature of your data.
The median equals the mean when the dataset is perfectly symmetric — meaning the values are evenly distributed around the center. This is the case for a normal (bell-curve) distribution. In such cases, the mean, median, and mode are all identical.