Average Calculator
Mean, median, mode, range and standard deviation — at once.
Show detailsHide details
'Average' can mean three different things — the mean, the median, or the mode — and they often disagree. Paste your numbers once and this calculator shows all three, plus the range, count, sum, and standard deviation, so you can see not just the typical value but how spread out your data is.
Loading calculator...
How to Calculate the Average — The Quick Answer
The everyday 'average' is the mean: add the values and divide by how many there are. But median (the middle value) and mode (the most common value) are also averages — and for skewed data the median is often the more honest one.
Shortcut
Mean = sum ÷ count | Median = middle value (sorted) | Mode = most frequent value | Range = max − min
Fact-Checking Claims You May Have Seen Online
The average always means the mean
Not quite
'Average' is an umbrella term for the mean, median, and mode. In everyday use it means the mean, but statisticians pick whichever best represents the data — often the median.
The mean is always the best 'typical' value
False
One extreme value drags the mean with it. Incomes of 20k, 22k, 25k and 500k have a mean of ~142k — a figure nobody earns. The median (23.5k) describes the group far better.
A bigger standard deviation means bigger numbers
False
Standard deviation measures spread, not size. {10, 10, 10} and {0, 10, 20} have the same mean (10) but very different spreads — the first is 0, the second is larger.
Worked on the set {2, 4, 4, 6, 9}
| Statistic | Value | How |
|---|---|---|
| Mean | 5 | (2+4+4+6+9) ÷ 5 = 25 ÷ 5 |
| Median | 4 | middle value of 2, 4, 4, 6, 9 |
| Mode | 4 | 4 appears twice; everything else once |
| Range | 7 | 9 − 2 |
| Std dev (sample) | 2.65 | spread around the mean, n − 1 |
| Std dev (population) | 2.37 | spread around the mean, n |
Mean vs median: use the mean for roughly symmetric data, and the median when a few very large or very small values would otherwise distort the picture (incomes, house prices, response times). The mode is most useful for categories and repeated values.
How It Works
The Formulas
What each statistic actually measures
Formula
Mean (x̄) = Σx ÷ n Median = middle value of the sorted list (mean of the two middle values if n is even) Mode = value(s) with the highest frequency Range = maximum − minimum Standard deviation (σ) = √( Σ(x − x̄)² ÷ n )
Variables
The arithmetic mean
Add every value and divide by the number of values. It uses all the data, which makes it precise but also sensitive to outliers — one extreme value shifts it noticeably.
The middle value
Sort the values and take the one in the middle. With an even count, average the two middle values. The median ignores how far away the extremes are, so it resists outliers.
The most frequent value
The value that appears most often. A data set can have one mode, several, or none (when every value is unique). It is the only average that works for non-numeric categories.
Standard deviation
The typical distance of a value from the mean. Divide the summed squared differences by n for a whole population, or by n − 1 for a sample drawn from a larger population (this tool shows both). A larger σ means more spread-out data.
Note: Sample vs population standard deviation: use the sample version (dividing by n − 1) when your numbers are a sample meant to represent a bigger group, and the population version (dividing by n) when your numbers are the entire group. For large n the two are almost identical.
Worked Example
The data set 2, 4, 4, 6, 9
Count and sum
There are 5 values. Sum = 2 + 4 + 4 + 6 + 9 = 25.
Mean
25 ÷ 5 = 5.
Median
Sorted: 2, 4, 4, 6, 9. The middle (3rd of 5) value is 4.
Mode
4 appears twice; every other value appears once — so the mode is 4.
Range
Maximum 9 − minimum 2 = 7.
Standard deviation
Squared differences from the mean (5): 9, 1, 1, 1, 16 = 28. Population: √(28 ÷ 5) ≈ 2.37. Sample: √(28 ÷ 4) ≈ 2.65.
Reference Guide
| unit | value | note |
|---|---|---|
| Mean | 5 | The arithmetic average |
| Median | 4 | The middle value |
| Mode | 4 | Appears twice |
| Range | 7 | 9 − 2 |
| Std dev (sample) | 2.65 | Divided by n − 1 |
| Std dev (population) | 2.37 | Divided by n |
Key Features
💡 Pro Tips
- →When the mean and median are far apart, your data is skewed — a few unusually large or small values are pulling the mean. Report the median in that case.
- →Pasting from a spreadsheet? A whole column (one number per line) works fine — the calculator ignores blank lines and non-numeric text.
- →Use population standard deviation only when your numbers are the entire group. If they are a sample standing in for a larger population, use the sample value.
- →A standard deviation of 0 means every value is identical. The bigger it gets relative to the mean, the more variable your data is.
Common Mistakes
Assuming 'average' always means the mean
Mean, median, and mode are all averages. For skewed data the mean can be misleading — the classic example is average income, where a few very high earners pull the mean well above what most people actually earn. The median is usually the fairer summary.
Confusing a wide range with high variability
The range only looks at the two most extreme values, so a single outlier can make it huge even when almost all the data is tightly clustered. Standard deviation, which uses every value, is a more reliable measure of spread.
Mixing up sample and population standard deviation
Dividing by n (population) slightly understates the spread when your data is only a sample of a larger group — that is why the sample formula divides by n − 1. Using the wrong one is a common statistics slip, though the gap shrinks as the data set grows.
Last updated: October 5, 2026
Creators
Computer Scientist & Developer Tools Author
Reviewers
Technical Reviewer
Table of Contents
Quick Facts
Privacy Guaranteed
Your data never leaves your browser. All calculations are 100% private.
Frequently Asked Questions
How do I calculate the average of a set of numbers?
For the mean (the everyday average), add all the numbers together and divide by how many there are. For 2, 4, 4, 6 and 9: the sum is 25 and there are 5 values, so the mean is 25 ÷ 5 = 5. Paste your own numbers above to get the mean along with the median, mode, range, and standard deviation.
What is the difference between mean, median, and mode?
The mean is the sum divided by the count. The median is the middle value when the numbers are sorted (the average of the two middle values if there is an even count). The mode is the value that appears most often. They are all 'averages', but they can give very different answers — especially when the data is skewed by a few extreme values.
When should I use the median instead of the mean?
Use the median when your data has outliers or is skewed — for example incomes, house prices, or response times. Because the median only depends on the middle of the sorted data, a few very large or very small values don't distort it the way they distort the mean.
What is standard deviation in simple terms?
Standard deviation is the typical distance between a value and the mean. A small standard deviation means the numbers are clustered tightly around the average; a large one means they are spread out. It is calculated as the square root of the average squared difference from the mean.
What's the difference between sample and population standard deviation?
Population standard deviation divides by n and is used when your numbers are the entire group you care about. Sample standard deviation divides by n − 1 and is used when your numbers are a sample representing a larger population — the n − 1 correction compensates for only seeing part of the whole. This calculator shows both.
Can a set of numbers have more than one mode, or none?
Yes. If two or more values tie for the most appearances, the set has multiple modes. If every value appears exactly once, there is no mode at all. This calculator lists every value that ties for most frequent, or tells you when there is no mode.