Average calculator.
Paste in a set of numbers and get the average instantly, along with the median, mode, range, sum, count and standard deviation. Every measure of your data set, worked out in one place.
Enter your data set
LiveSeparate values with commas, spaces or new lines. Decimals and negative numbers are fine; the full breakdown is below.
Average (mean)
18
of 6 numbers
Mean is the arithmetic average. See the median, mode, spread and more below. Calculations run in your browser; nothing you enter is stored.
How it works
The average, and beyond
The average, or mean, is the sum of your numbers divided by how many there are. The calculator also sorts the data to find the median, counts repeats to find the mode, and measures the spread with the range and standard deviation, so you see the whole picture, not just one number.
For 4, 8, 15, 16, 23 and 42, the sum is 108 and the count is 6, so the mean is 18. The median sits at 15.5, there is no repeated value so no mode, and the range is 38. Edit the box and every figure updates.
Every statistic
The full breakdown.
All the descriptive statistics for your data set, updating as you type. Sample figures use n minus 1; population figures use n.
Sorted, low to high
4, 8, 15, 16, 23, 42
The full guide
Mean, median, mode and spread.
Four ways to summarise a data set, what each one tells you, and when to reach for which.
What is the average (mean)?
The average, in everyday maths, means the arithmetic mean: add up all the numbers and divide by how many there are. For 2, 7, 19, 24 and 25, the sum is 77 and the count is 5, so the mean is 15.4. It is the single number that best represents a typical value when the data is fairly even.
The mean uses every value, which is its strength and its weakness. One very large or very small number can pull it noticeably up or down, so it is not always the most representative figure.
The median
The median is the middle value once the numbers are sorted. If there is an even count, it is the average of the two middle values. For 4, 8, 15, 16, 23 and 42, the two middle numbers are 15 and 16, so the median is 15.5.
Because it only cares about position, the median is barely affected by extreme values. That makes it the better summary for skewed data like incomes or house prices, where a few large numbers would distort the mean.
The mode
The mode is the value that appears most often. A data set can have one mode, several modes, or none at all if every value is unique. It is the only average that works for categories as well as numbers, such as the most common shoe size sold.
When every number in your set is different, the calculator reports no mode, which is correct rather than an error.
The range
The range is the simplest measure of spread: the largest value minus the smallest. For our example it is 42 minus 4, which is 38. It tells you how far the data stretches from end to end, but nothing about how the values sit in between.
Because it depends only on the two extremes, the range is sensitive to outliers, so it is best read alongside the standard deviation.
Standard deviation and variance
Standard deviation measures how spread out the numbers are around the mean. A small standard deviation means the values cluster close to the average; a large one means they are scattered widely. Variance is simply the standard deviation squared, and is the step used to calculate it.
There are two versions. The population version divides by the count, n, and is used when your numbers are the whole group. The sample version divides by n minus 1 and is used when your numbers are a sample drawn from a larger group. The calculator shows both so you can pick the right one.
Which average should you use?
Use the mean for roughly symmetric data with no extreme outliers, such as test scores. Use the median when the data is skewed or has outliers, such as salaries. Use the mode when you care about the most common category or value rather than a central number.
Reporting more than one is often the most honest approach. Showing the mean and the median together, for instance, quickly reveals whether a few large values are skewing the picture.
The formulas
Four numbers
for one data set.
The mean is sum over count. The median is the middle. The mode is the most frequent. Standard deviation measures the spread around the mean.
Try the percentage calculator ›# Mean (average)
mean = sum / count
# Median
middle value of the sorted list
(mean of the two middle if even)
# Range
range = max − min
# Standard deviation (population)
sd = √( Σ(x − mean)² / n )Questions
Average questions.
How do I calculate the average of a set of numbers?
+
Add all the numbers together, then divide by how many there are. For 2, 7, 19, 24 and 25, the sum is 77 and the count is 5, so the average is 15.4. Just paste your numbers into the box and the calculator does it for you.
What is the difference between mean, median and mode?
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The mean is the sum divided by the count. The median is the middle value when the numbers are sorted. The mode is the value that appears most often. They can all differ, especially when the data has outliers.
When should I use the median instead of the mean?
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Use the median when your data is skewed or has extreme values, such as incomes or house prices, because it is not pulled by outliers the way the mean is. For fairly even data, the mean is usually fine.
What is standard deviation?
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Standard deviation measures how spread out the numbers are around the mean. A small value means the data clusters near the average; a large value means it is scattered. The calculator shows both the sample version, dividing by n minus 1, and the population version, dividing by n.
Is this average calculator free and private?
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Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The average calculator computes standard descriptive statistics and is provided for everyday use and education.