Separate values with commas, spaces, semicolons or new lines. Use a dot for decimals.
How to use the Average Calculator
- 1Type or paste your numbers into the box, separated by commas, spaces, semicolons or new lines. A column copied from a spreadsheet works as is.
- 2Check the red notice, if one appears, for any entries that were ignored because they are not valid numbers.
- 3Read the mean (the ordinary average) in the highlighted box.
- 4Use the cards below it for the median, mode, range, count, minimum, maximum, sum and geometric mean.
- 5Press Clear to start again or Load example to restore the sample list.
Mean, median and mode explained
The mean is what most people call the average: add every value and divide by how many values there are. The median is the middle value once the list is sorted from smallest to largest; with an even number of values it is the halfway point between the two middle values. The mode is the value that appears most often. A list can have one mode, several modes, or no mode at all if no value repeats.
The range is the difference between the largest and smallest values, which gives a quick sense of how spread out the data is.
Worked example
Take the sample list 12, 15, 18, 15, 22, 30, 15, 18, 25. The nine values add up to 170, so the mean is 170 ÷ 9 ≈ 18.89. Sorted, the list is 12, 15, 15, 15, 18, 18, 22, 25, 30, and the fifth value, 18, is the median. The number 15 appears three times, more than any other, so it is the mode. The range is 30 − 12 = 18.
The geometric mean multiplies all values together and takes the nth root, which works out to about 18.18 here. It is always less than or equal to the ordinary mean and is only defined when every value is positive, so the calculator shows it only in that case.
Which average should you use?
Use the mean when values are fairly evenly spread, such as test scores in a class or daily temperatures. Use the median when a few extreme values could distort the picture. For five salaries of 30, 32, 35, 38 and 250 thousand, the mean is 77 thousand but the median is 35 thousand, which describes a typical salary far better. That is why house prices and incomes are usually reported as medians.
Use the mode for the most common choice or category, such as the most popular shoe size. Use the geometric mean for growth rates and ratios: if an investment grows 10% one year and 50% the next, the average yearly growth is about 28.45%, not 30%. To turn changes between two values into percentages first, our percentage calculator handles percentage increase and decrease.
Tips for entering data
Because commas separate values, do not use commas as thousands separators: type 12500 rather than 12,500, and use a dot for decimals. Negative numbers and scientific notation such as 1e3 are accepted. Blank lines and extra spaces are ignored.
If your values are fractions, convert them to decimals first with the fraction calculator.
Frequently asked questions
What is the difference between average and mean?
In everyday speech they mean the same thing: the sum of the values divided by how many there are. Strictly speaking, average is a broader word that can also refer to the median or mode, which is why statisticians prefer the more precise term arithmetic mean.
What happens if no number repeats?
Then the list has no mode and the calculator says so. It also reports no mode when every distinct value appears the same number of times, for example 1, 1, 2, 2, because no value is more common than the others.
How is the median found for an even number of values?
Sort the values and take the mean of the two in the middle. For 3, 7, 9 and 12 the middle values are 7 and 9, so the median is 8.
Why is the geometric mean not shown for my list?
The geometric mean uses logarithms or roots of the values, so it only exists when every value is greater than zero. If your list contains zero or a negative number, that card shows a short note instead.
Can I calculate a weighted average here?
Not directly, but you can approximate one by repeating values according to their weight, such as entering a grade twice if it counts double. Need test data to practise with? Generate a list with the random number generator and paste it straight in.