Enter a list of numbers to get the mean, median, mode, sum, count, and range. Steps are shown for each measure so you can see how every value is reached.
The average (mean) of a data set equals the sum of all values divided by the count of values, and it sits alongside the median and mode as one of three ways to describe the center of a list. Each tells you something different, and picking the wrong one can make a data set look more or less typical than it really is.
Notice that the mean (6.4) sits above the median (5) because the 12 pulls it upward. When a data set has outliers like this one, the median often gives a more honest picture of what a "typical" value looks like.
The median needs the list sorted first: for an odd count, it is the single middle value; for an even count, it is the average of the two middle values. The mode simply counts how often each value appears and reports whichever one appears most, with ties reported together and no repeats at all reported as "none."
For further reading on measures of central tendency, see the Wikipedia entry on average.
Once you have the center, spread is usually the next question worth asking.
Add all the numbers together, then divide by how many numbers there are. For example, the average of 3, 7, and 5 is (3 + 7 + 5) / 3 = 15 / 3 = 5.
Sum every value in your data set, then divide by the count of values. This gives the arithmetic mean, which is what most people mean by 'average'.
Step 1: add all numbers together to get the sum. Step 2: count how many numbers you have. Step 3: divide the sum by the count. The result is the mean average.
An average calculator takes a list of numbers and returns the mean (arithmetic average), median (middle value), mode (most common value), sum, count, and range in one step.
Marcus Vance spent a decade building data pipelines and testing calculation logic before he started writing about the math behind the tools. On MathCalcTools he checks every formula against the source math, then writes out the steps so a reader can follow the same path a calculator takes.