Statistics
Average Calculator
Find the average — the arithmetic mean — of any list of numbers. Paste your values and see the mean, median, mode, range, and spread recompute instantly, with the sum and division shown.
Enter your numbers
5 valuesSeparate with commas, spaces, or new lines.
Average (arithmetic mean)
30
sum 150 ÷ 5 values
mean = 150 ÷ 5 = 30
Median
30
Mode
none
Range
40
Std. dev (σ)
14.1421
Minimum
10
Maximum
50
Sorted
10, 20, 30, 40, 50
Updates as you type
Try an example
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The basics
What is an average?
An average is a single number that stands in for a whole list — its typical or central value. When people say “average” they almost always mean the arithmetic mean: add everything up, then divide by how many things there are. It is the fastest way to summarise a set of test scores, prices, or measurements in one figure.
mean = sum ÷ n
The formula
Add every value to get the sum, then divide by the count n. That single quotient is the mean — the balance point of the data.
(10 + 20 + 30 + 40) ÷ 4 = 25
Σx ÷ n
Why it works
The mean redistributes the total equally across all the items. If everyone in the set got the same share, that share would be the mean.
100 spread over 4 → 25 each
Method
How to calculate an average by hand
Three steps, however long the list.
- 1
Add the values together
Sum every number in the list. This total is sometimes written with the Greek letter sigma, Σ.
10 + 20 + 30 + 40 = 100 - 2
Count how many there are
Count the values to get n. Be careful to include every item — repeated values are counted each time they appear.
n = 4 - 3
Divide the sum by the count
Divide the total by the count. The quotient is the average — the arithmetic mean.
100 ÷ 4 = 25
Worked examples
The four kinds of mean
“Average” usually means the arithmetic mean, but there are three other means for special situations. Each is worked through below.
Given values = (4, 8, 15, 16, 23)
Add them up: 4 + 8 + 15 + 16 + 23 = 66
Divide by the count: 66 ÷ 5
mean = 13.2
The everyday average — equal weight to every value.
Three averages
Mean, median & mode
Statistics has three classic “averages,” each measuring the centre a different way. The calculator reports all three at once.
sum ÷ n
Mean
The arithmetic average. Uses every value, so it is sensitive to very large or very small ones.
2, 3, 3, 8 → 16 ÷ 4 = 4
middle value
Median
The middle of the sorted list. Resistant to outliers, which makes it the better choice for skewed data like incomes.
2, 3, 3, 8 → 3
most frequent
Mode
The value that occurs most often. The only average that also works for categories, not just numbers.
2, 3, 3, 8 → 3
Want the median and mode broken out on their own? Use the mean, median & mode calculator.
Where it shows up
Where averages are used
The average is the most-used statistic in daily life — a single number everyone understands.
grades
School & grades
Term grades and GPAs are averages of scores — often weighted so exams count more than homework.
per unit (USD)
Money & business
Average order value, average daily sales, and average price all condense many transactions into one tracking number.
°, km/h
Science & sport
Average temperature, average speed, and batting averages summarise repeated measurements over time.
Quick chart
What is the average of two numbers?
The average of two numbers is just their midpoint: add them and halve. Pick a first number to see its average with a range of second numbers.
First number
Second from
10 & 1
5.5
10 & 2
6
10 & 3
6.5
10 & 4
7
10 & 5
7.5
10 & 6
8
10 & 7
8.5
10 & 8
9
10 & 9
9.5
10 & 10
10
10 & 11
10.5
10 & 12
11
10 & 13
11.5
10 & 14
12
10 & 15
12.5
10 & 16
13
Average of two numbers = (a + b) ÷ 2 — the midpoint between them.
Worth knowing
Rules & pitfalls
A few properties of the mean are worth keeping in mind — and a couple of traps to avoid.
order doesn't matter
Order-independent
Rearranging the values never changes the mean, because addition is commutative. Order only matters for the median.
lies within range
Bounded by the data
The mean always sits between the smallest and largest values — it can never fall below the minimum or above the maximum.
outliers pull it
Sensitive to outliers
One extreme value drags the mean toward it. When data is skewed, report the median instead so a single outlier doesn't mislead.
don't average averages
Averages of averages
Averaging two means only works if both groups are the same size. Otherwise you need a weighted average that respects how many items each group holds.
empty set
No values, no mean
The mean of an empty list is undefined — you cannot divide by a count of zero. Always check there is at least one value.
balance point
The balancing centre
The mean is where the deviations cancel out: the distances of points above it exactly equal the distances of points below it.
Origins
A quick history of the average
The idea of dividing a total evenly is ancient, but the word “average” comes from maritime trade. Avaria was a medieval charge for goods damaged at sea; when cargo was thrown overboard to save a ship, the loss was shared proportionally among all the merchants. That fair-sharing of a total is exactly what the arithmetic mean does — spread the whole equally across every part. Astronomers later adopted the mean to combine repeated measurements and cancel out observational error, and it has been the default summary statistic ever since.
FAQ
Common questions
Add all the values together to get the sum, then divide that sum by how many values there are. For 10, 20, 30 and 40 the sum is 100 across 4 values, so the average is 100 ÷ 4 = 25.
In everyday use "average" means the arithmetic mean — the sum of the values divided by the count. The mean is one kind of average; the median (middle value) and the mode (most common value) are other averages used in statistics.
The mean is the sum divided by the count. The median is the middle value once the numbers are sorted. The mode is the value that appears most often. They can all differ for the same data set, and each describes the centre in a different way.
Add the two numbers and divide by 2 — the result sits exactly halfway between them. The average of 40 and 60 is (40 + 60) ÷ 2 = 50.
A weighted average lets some values count more than others. Multiply each value by its weight, add those products, then divide by the total of the weights. It is how grades, GPAs, and many index figures are calculated.
No. Addition does not depend on order, so the arithmetic mean is the same however you arrange the numbers. Order only matters for the median, which depends on sorting the values first.
A single very large or very small value pulls the mean toward it, which can make the mean unrepresentative. The median is resistant to outliers, so for skewed data — like incomes or house prices — the median is often the better average.
Sometimes, but not always with a plain mean. Averaging percentages of different-sized groups needs a weighted average, and averaging rates such as speed over equal distances needs the harmonic mean. Use a simple mean only when the items are equal and independent.
Keep going
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Keep reading
Further reading
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What Is the Mean? Definition, Formula, and How to Calculate It
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How to Calculate Standard Deviation in Excel
Use STDEV.S or STDEV.P in Excel, choose the right one for your data, and check the result against a worked example.
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How to Calculate Range in Statistics (Beginner’s Guide with Real-Life Examples)
A friendly, beginner-focused guide to understanding and calculating range in statistics. Learn what range means, how to compute it, real-life applications, and common mistakes to avoid.
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Written by
UC
Author
Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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