Mean Median Mode Calculator

When you have a list of numbers, a single summary value can help you understand the whole set at a glance. The mean, median, and mode are the three most common ways to describe the centre of data, and each tells you something slightly different. This calculator works out all three for you, along with the range, sum, count, and the smallest and largest values.

Paste in your numbers, press Calculate, and you will get clear results in seconds, with no sign-up and no sorting or adding by hand. If you are exploring more tools like this, our statistics calculators hub brings the full collection together in one place.

What Is the Mean Median Mode Calculator?

The mean median mode calculator is a free online tool that takes a list of numbers and calculates the main measures used to describe them. The mean is the usual average. The median is the middle value when the numbers are placed in order. The mode is the value that appears most often. Together, they give you a quick picture of a typical value in your data.

The tool also shows the range, sum, count, minimum, maximum, and your list sorted from smallest to largest, so you can check the median yourself. For a single average alone, try our average calculator.

How It Works and the Formulas

Mean. Mean = sum ÷ count. Add all the numbers together to get the sum, count how many numbers there are, then divide the sum by the count. For example, if the sum is 24 and there are 5 numbers, the mean is 24 ÷ 5 = 4.8. Every value affects the mean.

Median. The median is the middle value of the sorted list. First sort the numbers from smallest to largest. If the count is odd, the median is the single value in the middle. If the count is even, there is no single middle value, so add the two middle values and divide by 2. That result is the median.

Mode. The mode is the value that appears most often. If two values tie for the highest count, the data is bimodal and both are modes. If every value appears the same number of times, there is no mode. A list with only one distinct value, such as just 7, has that value as its mode here.

Range. Range = max − min. The maximum is the largest value and the minimum is the smallest value, so the range is the largest minus the smallest. It shows how spread out the data is: a small range means values are close together, a large range means they are spread widely.

How to Use the Mean Median Mode Calculator

1. Type or paste your numbers into the box, separated by commas, spaces, or new lines.
2. Check every entry is a number. Integers, decimals, and negatives are fine.
3. Press Calculate to see the mean, median, mode, range, sum, count, minimum, maximum, and sorted list.
4. Read the results together, using the interpretation guidance below.
5. Press Reset to clear the box and start again.

Worked Example

Use the list 2, 4, 4, 6, 8.

Step 1 — Sort: 2, 4, 4, 6, 8 (already in order).

Step 2 — Sum and count: 2 + 4 + 4 + 6 + 8 = 24, and the count is 5.

Step 3 — Mean: 24 ÷ 5 = 4.8.

Step 4 — Median: The count is odd, so the median is the middle (third) value: 4.

Step 5 — Mode: 4 appears twice, more than any other value, so the mode is 4.

Step 6 — Range: 8 − 2 = 6.

Result: sum 24, mean 4.8, median 4, mode 4, range 6.

Mean, Median and Mode Compared

Measure	What it tells you	When it is most useful	Weakness
Mean	The average when every value is shared out evenly	When values are fairly even, with no extreme outliers	One very large or small value can pull it a lot
Median	The middle value, with half the data below and half above	When data has outliers, such as incomes or house prices	Ignores the size of other values
Mode	The most common value	For the most frequent result, such as the most common shoe size sold	May be no mode, or several modes
Range	How spread out values are	For a quick sense of consistency	Uses only two values, so one outlier can mislead

If you need to turn a result into a share of a total, our percentage calculator can help with that next step.

Important Points and Assumptions

This calculator assumes your numbers are correct and complete. It does not guess missing values — if a token is not a number, it shows an error naming that token. A mean or median may be a decimal even when all inputs are whole numbers.

Each entry is treated equally, with no weights. If some values should count more, a weighted average is more suitable. For checking related maths, our scientific calculator is also useful.

Common Mistakes

Forgetting to sort before finding the median. The middle entry of an unsorted list is often not the median.

Reporting one mode when data is bimodal. If two values tie for the highest count, both are modes.

Claiming a mode when there is none. If every value appears the same number of times, there is no mode.

Trusting the mean alone with outliers. One extreme value can drag the mean away from most of the data, so compare it with the median.

Miscounting. A missing or extra number changes the sum, count, mean, and median. Check the count in the results.

How to Interpret Your Results

Compare the mean and median first. If they are close, the data is fairly balanced. If the mean is much higher, large values are pulling it up; if much lower, small values are pulling it down. Then the median is often the better guide to a typical value.

Next look at the mode for the most common value, and the range for spread. A small range means consistency; a large range warns that one centre value may not describe the set well.

Frequently Asked Questions

What is the difference between the mean and the median?

The mean is the sum divided by the count, so every value affects it. The median is the middle value of the sorted list, so extreme values have little effect on it.

Can a set of numbers have more than one mode?

Yes. If two values tie for the highest count, the data is bimodal and both are modes. More than two tied values is called multimodal. This calculator lists all modes.

What does it mean if there is no mode?

Every value appears the same number of times, so none is more common than the others. For example, 1, 2, 3 has no mode because each value appears once.

How do you find the median with an even number of values?

Sort the list, add the two middle values, and divide by 2. In 1, 2, 3, 4, the middle values are 2 and 3, so the median is (2 + 3) ÷ 2 = 2.5.

Can I enter decimals and negative numbers?

Yes. Decimals such as 4.5 and negatives such as -3 are accepted, separated by commas, spaces, or new lines.

Why did I get an error message?

A token in your list was not a number, or the box was empty. The message names the bad token, for example “five”, so you can replace it with 5 and try again.

References

For standard definitions of summary statistics, see the NIST/SEMATECH e-Handbook of Statistical Methods.