📊 Average Calculator
Enter a list of numbers to instantly compute the mean, sum, count, median, minimum, maximum, range, and more — separated by commas, spaces, or new lines.
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Mean / Average
sum ÷ count
Sum
total
Count
numbers
Minimum
smallest
Maximum
largest
Median
middle value
Range
max − min
Std Deviation
population
Mode
most frequent
Min:
Mean position in range
Max:
Mean () is at % of the range
Sorted Numbers
Minimum
Maximum
Export results:
📐
Mean
Arithmetic average of all values
➕
Sum
Total of all numbers added together
#
Count
How many numbers were entered
📊
Median
Middle value when sorted
⬇️
Min
Smallest number in the list
⬆️
Max
Largest number in the list
Related Calculators
From a pasted list to nine statistics
The tool first parses your input into numbers, counting valid entries and flagging anything it cannot read. The sum is the running total of the valid values, and the count is how many there are. The mean is simply the sum divided by the count, which is the arithmetic average most people mean by the word.
For the median the values are sorted. When the count is odd, the median is the value sitting in the middle position. When the count is even, there is no single middle value, so the tool takes the two central values and averages them. The minimum and maximum are then just the first and last entries of the sorted list, and the range is the maximum minus the minimum.
The mode is found by tallying how often each distinct value appears and keeping every value that hits the highest tally. If every value appears exactly once, there is no mode and the tool says so rather than inventing one. Standard deviation is calculated as the population standard deviation: each value's distance from the mean is squared, those squares are averaged over the full count, and the square root of that average is taken.
For the median the values are sorted. When the count is odd, the median is the value sitting in the middle position. When the count is even, there is no single middle value, so the tool takes the two central values and averages them. The minimum and maximum are then just the first and last entries of the sorted list, and the range is the maximum minus the minimum.
The mode is found by tallying how often each distinct value appears and keeping every value that hits the highest tally. If every value appears exactly once, there is no mode and the tool says so rather than inventing one. Standard deviation is calculated as the population standard deviation: each value's distance from the mean is squared, those squares are averaged over the full count, and the square root of that average is taken.
Six values run through every statistic
Take the list 4, 8, 15, 16, 23, 42. The sum is 108 and the count is 6, so the mean is 108 divided by 6, which is 18 exactly.
Sorted, the list is already in order. With six values the median averages the third and fourth entries: 15 plus 16 is 31, divided by 2 gives 15.5. The minimum is 4 and the maximum is 42, so the range is 38. Every value appears once, so the tool reports no mode.
Standard deviation takes longer by hand. The distances from the mean of 18 are minus 14, minus 10, minus 3, minus 2, plus 5 and plus 24. Squaring each gives 196, 100, 9, 4, 25 and 576, which total 910. Dividing 910 by the count of 6 gives a variance of 151.667, and the square root of that is 12.32 to two decimal places.
Notice that the mean of 18 sits above four of the six values. The single reading of 42 is pulling it upward, which is exactly the kind of skew the median of 15.5 reveals.
Sorted, the list is already in order. With six values the median averages the third and fourth entries: 15 plus 16 is 31, divided by 2 gives 15.5. The minimum is 4 and the maximum is 42, so the range is 38. Every value appears once, so the tool reports no mode.
Standard deviation takes longer by hand. The distances from the mean of 18 are minus 14, minus 10, minus 3, minus 2, plus 5 and plus 24. Squaring each gives 196, 100, 9, 4, 25 and 576, which total 910. Dividing 910 by the count of 6 gives a variance of 151.667, and the square root of that is 12.32 to two decimal places.
Notice that the mean of 18 sits above four of the six values. The single reading of 42 is pulling it upward, which is exactly the kind of skew the median of 15.5 reveals.
Picking the right average and reading the spread
Mean, median and mode answer different questions. The mean is the balance point and uses every value, which makes it sensitive to extremes. The median is the middle position and barely moves when one reading is unusual, which is why house prices and salaries are usually reported as medians. The mode is the most common value, and it is the only one of the three that works for categories rather than quantities. When mean and median are far apart, as in the example above, the distribution is skewed and quoting the mean alone will mislead.
Standard deviation here is the population version, which divides the squared distances by the full count. If your numbers are a sample drawn from a larger group and you want to estimate that group's spread, statisticians normally divide by the count minus one instead, producing a slightly larger figure. For a complete set of data, such as every mark in one class, the population figure is the correct one.
Check the valid and invalid counts before trusting the output. Currency symbols, thousands separators and stray text can leave entries unread.
Standard deviation here is the population version, which divides the squared distances by the full count. If your numbers are a sample drawn from a larger group and you want to estimate that group's spread, statisticians normally divide by the count minus one instead, producing a slightly larger figure. For a complete set of data, such as every mark in one class, the population figure is the correct one.
Check the valid and invalid counts before trusting the output. Currency symbols, thousands separators and stray text can leave entries unread.
Frequently Asked Questions
The parser reads a list and reports how many entries it recognised as valid and how many it could not read, so you can paste a column copied from a spreadsheet or a separated list and then check the valid count against the number of values you expected before relying on the results.
Population standard deviation. The squared deviations from the mean are divided by the total count rather than by the count minus one. That is the right choice when your list is the complete set of data. For a sample used to estimate a wider group, the sample version would return a marginally larger number.
The tool reports that there is no mode. A mode only exists when at least one value occurs more often than the others. If several values tie for the highest frequency, the calculator treats all of them as modes rather than arbitrarily picking one, so a list can legitimately be multimodal.
Because the mean is affected by extreme values and the median is not. One very large or very small reading drags the mean towards it while leaving the middle position almost untouched. A wide gap between the two is a reliable sign that your data is skewed and that the median describes it better.
Yes. There is a decimal places setting with an automatic option alongside fixed choices, so you can present results to the precision your work requires. Changing it affects the display only; the underlying calculations always run at full precision, so rounding never accumulates between statistics.