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Average Calculator

Written by:
PK

Below is an average calculator, which will calculate the arithmetic mean from a list of numbers. Enter any type of number including decimals or negative, separated with any non-number and the tool will return the average.

Looking for a different tool? Instead try one of the related statistic calculators:

Average Calculator

What is the Average or Arithmetic Mean?

The average (or the mean) of a set of numbers is one number that represents or summarizes the whole set. Colloquially, we say it is a measure of the central tendency of the numbers – most often along with the median (number in the 'middle' of the set after ordering) and mode (number(s) that appear most in the set).

Most commonly, average is the arithmetic mean – the number you get when adding all the numbers in the set then dividing by the length of the set. The arithmetic average is not the only average, though – in fact, there are many types:

  • Geometric mean – the average you get when multiplying n numbers in a set together then taking the set's nth root. Geometric average is very useful in financial returns (see our investment calculators for examples).
  • Harmonic mean – the average you get when dividing the length of a set of (importantly, non-zero) numbers by the sum of their reciprocals. This is very useful for speed calculations.
  • Other means – for example the root mean square (RMS) or quadratic mean, used, for example, in alternating current voltage math (i.e. "120 volts" or "240 volts" for appliances).

Again, this isn't an exhaustive set of means. Usually, if you're in a field you'll know where a mean is warranted versus another – but hope this overview was interesting!

Formula for Arithmetic Average

The formula for the arithmetic average is:

average = \frac{a_1+a_2+...+a_{n-1}+a_n}{n}

Written as a series, it is:

average=\frac{1}{n}\sum_{i-1}^{n} a_i

If that looks like nonsense, don't worry – to get the arithmetic average, you simply add up every number in a set, then divide by the number of numbers in the set. Let's work through an example together.

Example Average Calculation

Let's say you want to take the average of 5 numbers: -3, 4, 7, 7.5, and 500. Here's how it works:

\frac{-3+4+7+7.5+500}{5}=\\\frac{515.5}{5}=103.1

Using the Average Calculator

In the text box at the top, enter a list of numbers to average. When happy, simply hit the Compute Average button below and DQYDJ will find the arithmetic average.

This calculator was built to be forgiven on inputs. Enter your numbers with any sort of non-number in between them – tabs, commas, new lines, etc. You can verify we understood your input by seeing how many values we found in the Number of Values Input field.

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