Using the calculator
Type or paste your numbers, separated by commas, spaces or new lines. Decimals and negative numbers are fine, and a column copied from a spreadsheet works too. All four results appear straight away. Below them are the count, the sum and the smallest and largest values.
The working lists the numbers in order and then finds each result in turn. The dot plot stacks repeated values, so the mode is the tallest column, and dashed lines mark the mean and the median.
The three averages
The mean is what most people call the average. Add up the numbers and divide by how many there are. For the six numbers in the box the total is 29, and 29 ÷ 6 is about 4.83.
The median is the middle value once the numbers are in order. With an odd count there is one middle number. With an even count there are two, and the median is halfway between them. In order, the list above is 1, 2, 3, 7, 7, 9, so the median is halfway between 3 and 7, which is 5.
The mode is the value that appears most often, here 7. A list can have two modes, or more, when values tie. If every value appears equally often, there is no mode.
Which average to use
The mean uses every value, so one very large or very small number pulls it a long way. The median only cares about the middle, so it stays put. Add 100 to the list above and the mean jumps from about 4.83 to about 18.4, while the median only moves from 5 to 7.
The mode is the only one of the three that works for things that aren't numbers, such as the most popular shoe size or favourite colour. The range, largest minus smallest, is the simplest measure of how spread out the numbers are. For a better one, use the standard deviation calculator.
Questions
Is the average the same as the mean?
Usually. In everyday speech the average means the mean. Strictly, the median and mode are averages too, since each is a way of describing a typical value.
What if there are two modes?
Then the data is bimodal, and both are modes. The calculator lists every value that ties for most often.
How do I find the median of an even number of values?
Put them in order, take the two in the middle, add them and halve the result. For 2, 4, 6, 8 the middle two are 4 and 6, so the median is 5.
How many decimal places does it show?
Results are rounded to 2 decimal places, and the working says when the mean has been rounded. The sum and the smallest and largest values are shown in full.
Are my numbers sent anywhere?
No. The calculations run in your browser.
Sources
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