How to calculate an average
In everyday use, average usually means the arithmetic mean. Add all values together and divide the sum by the number of values.
For example, consider the values 12, 15, 15, 18, 21 and 30. Their sum is 111 and there are six values.
Mean vs. median
The mean uses every value in the data set. The median instead identifies the middle of the sorted data.
For an odd number of values, the median is the single middle value. For an even number of values, the median is the average of the two middle values.
The example data sorts to 12, 15, 15, 18, 21 and 30. The two middle values are 15 and 18, so:
What is the mode?
The mode is the value that appears most often. In the example, 15 occurs twice while every other value occurs once, so the mode is 15.
A list does not necessarily have a mode. If every value occurs the same number of times, this calculator reports no mode.
A data set can also have multiple modes. If two or more values share the highest frequency, the calculator lists each tied value.
What is the range?
The range measures the distance between the smallest and largest values.
For the example values, the maximum is 30 and the minimum is 12, giving a range of 18.
Sum and count
The calculator shows both the total sum and the number of values used. These are useful for checking the arithmetic mean because the mean is simply the sum divided by the count.
Population standard deviation
Standard deviation describes how spread out the values are around their mean. A smaller standard deviation indicates values clustered more closely around the mean, while a larger value indicates greater spread.
Population standard deviation treats the entered values as the complete population.
Sample standard deviation
Sample standard deviation is used when the entered data is a sample drawn from a larger population. It divides the sum of squared deviations by n − 1 rather than n.
Sample standard deviation requires at least two values, so it is not available for a one-number data set.
How to enter numbers
You can separate values with commas, spaces, semicolons or new lines. This makes it easy to paste a column of numbers from a spreadsheet or enter a short list manually.
Decimals, whole numbers, zero and negative values are all supported.
Example with negative numbers
Suppose the values are -5, -2, 0, 3 and 9. Their sum is 5 and the count is 5, so the mean is 1. The median is 0 because it is the middle value after sorting.
When mean and median differ
A very large or very small outlier can pull the arithmetic mean toward the extreme value. The median depends only on the middle position and is therefore less affected by extreme observations.
For example, the data 2, 2, 3, 4 and 100 has a mean of 22.2 but a median of 3. Both values are calculated correctly; they describe the center in different ways.
Average vs. percentage
An average combines several numeric values into a measure of central tendency. A percentage describes a value relative to 100.
For percentage calculations, use the Percentage Calculator.
Average vs. ratio
A ratio compares the relative size of two quantities. It does not calculate the arithmetic mean of a list.
To simplify or scale ratios, use the Ratio Calculator.
How the calculator handles modes
The calculator counts how many times each numeric value occurs. If the highest frequency is only one, the result is shown as no mode. If several values tie for the highest frequency above one, all of them are treated as modes.
Rounding and precision
Calculations use the numeric values entered in your browser. Results are displayed with sensible decimal formatting, while the underlying calculations use JavaScript number precision.
Privacy
The list of numbers is processed directly by the calculator in your browser. There is no form submission required to obtain the statistical results.
Mean, median, mode and standard deviation describe different characteristics of a data set. The most useful measure depends on the data and the purpose of the analysis.
Frequently asked questions
Is average the same as mean?
In common arithmetic usage, average usually refers to the arithmetic mean: the sum of all values divided by the number of values.
Can a data set have more than one mode?
Yes. Two or more values can tie for the highest frequency, producing multiple modes.
What if every number is different?
If every entered value appears only once, this calculator reports no mode.
Can I enter negative numbers and decimals?
Yes. Both negative values and decimal values are supported.
What is the difference between sample and population standard deviation?
Population standard deviation treats the entered values as the complete population. Sample standard deviation treats them as a sample and uses n − 1 in the variance calculation.
Using this calculator effectively
The Average Calculator finds the arithmetic mean of a list of numbers and also reports the median, mode, range, sum, count, minimum, maximum and standard deviation. It supports whole numbers, decimals and negative values.
Common uses
- Finding the average of test scores, measurements, prices, times or other numeric observations.
- Comparing mean and median when a data set contains unusually high or low values.
- Checking modes, range and standard deviation alongside the arithmetic average.
Tips for a better estimate
- Paste only the observations that belong in the data set you want to analyze.
- Use the sample standard deviation when the entered observations are a sample of a larger population.
- Remember that a large outlier can substantially change the arithmetic mean even when the median changes little.
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