Average Calculator

Type or paste a list of numbers and see the average (mean) at once, with the median, mode, range, standard deviation, variance, quartiles and geometric mean beside it. The working is written out below: the sum divided by the count, the ordered list with the middle marked, the most common value, and each step of the standard deviation, for a sample or a whole population. Switch to Weighted average for values that count for different amounts, such as grades worth different percentages.

How it works

Average Calculator is a web page that does its work on your own device. Everything you type or choose is worked out by your browser and never sent to a server, so nothing is stored and there is nothing to delete. There is no account, no sign-up and no limit on how often you use it.

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Mean, Median, Mode Calculator · Standard Deviation Calculator · Weighted Average Calculator

Mean, median and mode

The mean is what most people call the average: add the numbers and divide by how many there are. The median is the middle number once they are in order, or the average of the two middle numbers when there is an even count. The mode is the number that comes up most often; a list can have several modes, or none when every number appears once. The range is the largest minus the smallest.

For 12, 15, 11, 15, 18, 20 and 14 the sum is 105, so the mean is 105 ÷ 7 = 15. In order the list is 11, 12, 14, 15, 15, 18, 20, so the median is the fourth number, 15. The mode is 15, which appears twice, and the range is 20 − 11 = 9.

Which average to use

The mean uses every number, so one very large or small value pulls it a long way: a single house sale of $3 million in a street of $300,000 homes doubles the mean but barely moves the median. That is why house prices and incomes are usually given as medians. The mode suits things you count rather than measure, such as the most common shoe size.

Standard deviation

Standard deviation measures how spread out the numbers are around the mean. Take each number's distance from the mean, square it, add the squares up, divide, and take the square root. Divide by n − 1 when your numbers are a sample drawn from something bigger, such as 30 customers out of thousands; divide by n when they are the whole population, such as every student in one class. The sample version is the default in most courses and in spreadsheet functions such as STDEV; the population version matches STDEV.P.

Quartiles

The lower quartile (Q1) is the median of the lower half of the ordered list and the upper quartile (Q3) the median of the upper half, leaving out the middle number when the count is odd. This is the method taught in most US schools and used by graphing calculators; spreadsheets use other methods and can give slightly different quartiles for small lists.

Weighted average

When some values count for more than others, multiply each value by its weight, add those products and divide by the total of the weights. Grades of 90, 85 and 78 worth 30%, 30% and 40% give (90 × 30 + 85 × 30 + 78 × 40) ÷ 100 = 83.7, lower than the plain average of 84.3 because the lowest grade carries the most weight.

What it does

• Mean, median, mode and range
• Standard deviation and variance, sample or population
• Quartiles, sum, count, smallest, largest, geometric mean
• Every step written out, with the middle of the ordered list marked
• Paste a column from a spreadsheet
• Weighted average with any weights

Questions

How do I find the average of a set of numbers?

Add them up and divide by how many there are. The average of 12, 15, 11, 15, 18, 20 and 14 is 105 ÷ 7 = 15.

What is the difference between mean, median and mode?

The mean is the sum divided by the count, the median is the middle value once they are in order, and the mode is the value that appears most often.

How do I find the median of an even number of values?

Put them in order and average the two middle ones. For 3, 5, 8 and 10, the median is (5 + 8) ÷ 2 = 6.5.

Can there be more than one mode, or none?

Yes. If two values tie for most common, both are modes. If every value appears once, there is no mode.

Should I use the sample or population standard deviation?

Use the sample (n − 1) when your numbers are a sample from a bigger group, which is the usual case in class and in spreadsheets (STDEV). Use the population (n) when you have every member of the group (STDEV.P).

How do I work out a weighted average?

Multiply each value by its weight, add the results and divide by the sum of the weights. 90, 85 and 78 weighted 30, 30 and 40 give 83.7.

Is anything sent anywhere?

No. The working runs in your browser and nothing you type is sent to us or stored.

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