Mean Calculator

Enter a list of numbers to find their arithmetic mean (average), along with the sum, count, and range of the data set.

Quick Facts

Mean formula
x̄ = (Σx) / n
Add every value, then divide by how many values there are.
Sensitive to outliers
Every value counts
One very large or small value can pull the mean noticeably; the median resists this better.
Population vs. sample
μ (population) vs. x̄ (sample)
Same formula, different symbol depending on whether you used the whole population or a sample.

Your Results

Calculated
Arithmetic Mean
-
x̄ = sum ÷ count
Sum of Values
-
Σx, the total of all entries
Count of Values
-
n, the number of entries
Range
-
Max − min, the spread of the data

Ready

Enter two or more numbers, then press Calculate.

Formula and Method for the Mean Calculator

The arithmetic mean — usually just called "the mean" or "the average" — is the most common measure of central tendency in a data set. It is found by adding up every value and dividing by how many values there are: x̄ = (x1 + x2 + ... + xn) / n, often written more compactly as x̄ = (Σx) / n, where Σx is the sum of all the values and n is the count of values. This calculator also reports the sum, count, and range of your data set so you can see the underlying numbers behind the mean.

Formula and method

Enter your numbers separated by commas or spaces. The calculator parses each entry, adds them together to get the sum (Σx), counts how many entries there are (n), and divides the sum by the count to get the mean: x̄ = Σx / n. It also finds the smallest and largest values in your list and reports their difference as the range, which gives a quick sense of how spread out the data is.

Common sources of error

  • Mixing units: the mean only makes sense if every value is measured in the same unit — convert everything to one unit before entering the list.
  • Confusing mean with median or mode: the mean is the sum divided by the count; it is not the middle value (median) or the most frequent value (mode), and the three can differ significantly on skewed data.
  • Forgetting an outlier's pull: because every value contributes to the sum, one unusually large or small number can shift the mean far from what most of the data looks like.

Checking your result

A quick sanity check: the mean should always fall between the smallest and largest values in your list — if it does not, recheck your entries for a typo or a misplaced decimal point. For a small, roughly symmetric data set, the mean should also land reasonably close to the middle of the sorted values.

Applications

The arithmetic mean is used to summarize test scores, average monthly expenses, typical measurements in a lab, average ratings, and countless other data sets where values simply add together. Because it uses every data point, it is the standard "average" for symmetric data, while the median is often preferred when a few extreme values (outliers) would otherwise distort the picture.

Frequently Asked Questions

What is the formula for calculating the mean?
The arithmetic mean (average) is the sum of all the values divided by how many values there are: x̄ = (x1 + x2 + ... + xn) / n. For example, the mean of 4, 8, and 12 is (4 + 8 + 12) / 3 = 8.
What is the difference between mean, median, and mode?
The mean is the sum of all values divided by the count. The median is the middle value when the data is sorted (or the average of the two middle values for an even count). The mode is the value that appears most often. They can all differ for the same data set, especially when the data is skewed.
How does an outlier affect the mean?
Because the mean uses every value in its sum, a single very large or very small outlier can pull it noticeably higher or lower. The median is far less sensitive to outliers, which is why skewed data sets (like incomes) are often summarized with the median instead of the mean.
What is the difference between a population mean and a sample mean?
Both use the same formula, sum divided by count, but the population mean (symbol μ) uses every member of the full population, while the sample mean (symbol x̄) uses only a subset drawn from that population and is used to estimate μ.

Related calculators