What is the difference between mean, median and mode?

They are three ways to describe the middle of a set of numbers. The mean adds the numbers and divides by the count. The median is the middle value of the sorted list. The mode is the value that appears most often. For 2.5, 3, 3, 4.1, 5, 7.4, 9 the mean is ≈ 4.857143, the median is 4.1 and the mode is 3.

How do I calculate the average of a list of numbers?

Add all the numbers and divide the sum by how many numbers there are. For 2.5, 3, 3, 4.1, 5, 7.4, 9 the sum is 34, there are 7 numbers, and 34 ÷ 7 = ≈ 4.857143. The calculator writes this working out under the result.

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

Sort the numbers and take the mean of the two in the middle. For 4, 8, 15, 16, 23, 42 the middle two are 15 and 16, so the median is (15 + 16) ÷ 2 = 15.5. With an odd count the median is simply the middle number. The sorted list under the result highlights the middle value or values.

Can a list have more than one mode, or none?

Yes. 1, 2, 2, 3, 3, 4 has two modes, 2, 3, because both appear twice. When every value appears exactly once, as in 4, 8, 15, 16, 23, 42, there is no mode, and the calculator says “No mode” rather than naming a value.

When is the median better than the mean?

When a few extreme values would pull the mean away from what is typical. For 10, 20, 30, 40, 1000 the mean is 220, which is bigger than four of the five numbers, while the median is 30. That is why incomes and house prices are usually quoted as medians.

What is the difference between sample and population standard deviation?

Both measure how far the numbers typically sit from the mean. The population version divides the sum of squared distances by the count n, and is right when your list is every value you care about. The sample version divides by n − 1 and is right when the list is a sample from a larger group. For 2.5, 3, 3, 4.1, 5, 7.4, 9 they are ≈ 2.472419 (sample) and ≈ 2.289015 (population). A single number has no sample standard deviation.

How does the weighted average work?

Each value counts in proportion to its weight. Multiply every value by its weight, add the products, and divide by the total of the weights. A course graded 90 (weight 40), 80 (weight 30) and 70 (weight 30) averages 81, while the plain mean of 90, 80 and 70 is 80. The weights only need to be in proportion, so 40, 30, 30 and 4, 3, 3 give the same answer.

How are commas treated: 1,234 or 1,2,3?

A comma is a separator, except when it can only be a thousands separator: a run with no spaces made of 1-3 digits followed by groups of exactly three digits after a comma is one number. So 1,234 is the one number one thousand two hundred thirty-four (the minimum of 1,234 5,678 9,012 is 1,234), 1,2,3 is three numbers, and 1, 234 (with a space) is two. A decimal comma such as 3,5 is not supported and is read as 3 and 5; use a point for decimals.

What happens to text and other things that are not numbers?

They are left out and listed under the input, never silently dropped. For “12, 15, n/a, 18, abc” the calculator averages 12, 15 and 18 (15) and reports that “n/a” and “abc” were ignored. A currency symbol, a plus or minus sign and a trailing percent sign are accepted and dropped, so $5 reads as 5 and 20% as 20.

Why does the calculator show 0.3 for 0.1 + 0.2?

Most programs add decimals as binary floating-point numbers, where 0.1 + 0.2 is 0.30000000000000004. This calculator reads every number as an exact decimal and adds whole numbers, so the sum of 0.1 and 0.2 is 0.3 and their mean is 0.15. Results are shown in full when they end within 12 decimals and otherwise rounded to 6 decimals with a ≈ in front.

Is there a limit on how many numbers I can enter?

The calculator reads up to 200,000 numbers, each with up to 30 digits, and says so if more were pasted. Ten thousand numbers are worked out instantly in your browser, and nothing you enter is sent anywhere.

Average Calculator

The average (mean) is the sum of the numbers divided by how many there are: for 2.5, 3, 3, 4.1, 5, 7.4, 9 the sum is 34 and the mean is ≈ 4.857143. The median is the middle number once they are sorted (4.1), the mode is the value that appears most often (3), and the range is the largest minus the smallest (6.5). Paste numbers separated by commas, spaces or new lines, or a column from a spreadsheet; the calculator also gives the standard deviation, a weighted average (90 40; 80 30; 70 30 gives 81) and shows the working for the mean and the median.

Updated 2026-10-03Runs in your browser: nothing you enter is uploadedHow this tool works

Average of 7 numbers

Mean ≈ 4.857143

Median 4.1, mode 3, range 6.5.

Count: 7
Sum: 34
Mean (average): ≈ 4.857143
Median: 4.1
Mode: 3 (appears 2 times)
Range: 6.5
Minimum: 2.5
Maximum: 9
Sample standard deviation: ≈ 2.472419
Population standard deviation: ≈ 2.289015

Mean: the working

Add up the 7 numbers: 2.5 + 3 + 3 + 4.1 + 5 + 7.4 + 9 = 34.
Divide the sum by the count: 34 ÷ 7 = ≈ 4.857143.

Median: the working

Sort the numbers from smallest to largest.
There are 7 numbers (an odd count), so the median is the middle one, number 4: 4.1.

2.5, 3, 3, 4.1, 5, 7.4, 9

Mean, median, mode and range worked out

Each row is the calculator’s own answer for the numbers in the first column.
Numbers	Count	Mean	Median	Mode	Range
2.5, 3, 3, 4.1, 5, 7.4, 9	7	≈ 4.857143	4.1	3	6.5
4, 8, 15, 16, 23, 42	6	18	15.5	No mode	38
1, 2, 2, 3, 3, 4	6	2.5	2.5	2, 3	3
10, 20, 30, 40, 1000	5	220	30	No mode	990
-5, -2, 0, 3, 4	5	0	0	No mode	9
0.1, 0.2	2	0.15	0.15	No mode	0.1
1,234 5,678 9,012	3	5,308	5,678	No mode	7,778

Which average should you use?

Shown for 2.5, 3, 3, 4.1, 5, 7.4, 9.
Measure	How it is found	Best when	Result
Mean	Sum ÷ count	The values are fairly even, with no extreme outliers	≈ 4.857143
Median	Middle of the sorted list	A few extreme values would drag the mean (incomes, house prices)	4.1
Mode	Most frequent value	The data are categories or repeated whole values (shoe sizes)	3
Range	Maximum − minimum	You want a quick sense of the spread	6.5
Standard deviation	Typical distance from the mean	You want a spread that uses every value	≈ 2.472419 (sample)

How to find the mean, median, mode and range

List the numbers. Type or paste them, separated by commas, spaces, tabs or new lines. A pasted spreadsheet column works as it is. 2.5, 3, 3, 4.1, 5, 7.4, 9 has 7 numbers.
Find the mean. Add the numbers and divide by how many there are: 34 ÷ 7 = ≈ 4.857143.
Find the median. Sort the numbers. With an odd count the median is the middle one; with an even count it is the mean of the two middle ones. For 4, 8, 15, 16, 23, 42 that is (15 + 16) ÷ 2 = 15.5.
Find the mode. Count how often each value appears. The most frequent value is the mode, and there can be more than one: 1, 2, 2, 3, 3, 4 has the modes 2, 3. If every value is different there is no mode.
Find the range. Subtract the smallest number from the largest: 9 − 2.5 = 6.5.
Weight the numbers when they count unequally. Switch the input to “Weighted” and give one value and its weight per line. Multiply each value by its weight, add them and divide by the total weight: 90 40; 80 30; 70 30 gives 81.

Frequently asked questions

What is the difference between mean, median and mode?: They are three ways to describe the middle of a set of numbers. The mean adds the numbers and divides by the count. The median is the middle value of the sorted list. The mode is the value that appears most often. For 2.5, 3, 3, 4.1, 5, 7.4, 9 the mean is ≈ 4.857143, the median is 4.1 and the mode is 3.
How do I calculate the average of a list of numbers?: Add all the numbers and divide the sum by how many numbers there are. For 2.5, 3, 3, 4.1, 5, 7.4, 9 the sum is 34, there are 7 numbers, and 34 ÷ 7 = ≈ 4.857143. The calculator writes this working out under the result.
How do you find the median of an even number of values?: Sort the numbers and take the mean of the two in the middle. For 4, 8, 15, 16, 23, 42 the middle two are 15 and 16, so the median is (15 + 16) ÷ 2 = 15.5. With an odd count the median is simply the middle number. The sorted list under the result highlights the middle value or values.
Can a list have more than one mode, or none?: Yes. 1, 2, 2, 3, 3, 4 has two modes, 2, 3, because both appear twice. When every value appears exactly once, as in 4, 8, 15, 16, 23, 42, there is no mode, and the calculator says “No mode” rather than naming a value.
When is the median better than the mean?: When a few extreme values would pull the mean away from what is typical. For 10, 20, 30, 40, 1000 the mean is 220, which is bigger than four of the five numbers, while the median is 30. That is why incomes and house prices are usually quoted as medians.
What is the difference between sample and population standard deviation?: Both measure how far the numbers typically sit from the mean. The population version divides the sum of squared distances by the count n, and is right when your list is every value you care about. The sample version divides by n − 1 and is right when the list is a sample from a larger group. For 2.5, 3, 3, 4.1, 5, 7.4, 9 they are ≈ 2.472419 (sample) and ≈ 2.289015 (population). A single number has no sample standard deviation.
How does the weighted average work?: Each value counts in proportion to its weight. Multiply every value by its weight, add the products, and divide by the total of the weights. A course graded 90 (weight 40), 80 (weight 30) and 70 (weight 30) averages 81, while the plain mean of 90, 80 and 70 is 80. The weights only need to be in proportion, so 40, 30, 30 and 4, 3, 3 give the same answer.
How are commas treated: 1,234 or 1,2,3?: A comma is a separator, except when it can only be a thousands separator: a run with no spaces made of 1-3 digits followed by groups of exactly three digits after a comma is one number. So 1,234 is the one number one thousand two hundred thirty-four (the minimum of 1,234 5,678 9,012 is 1,234), 1,2,3 is three numbers, and 1, 234 (with a space) is two. A decimal comma such as 3,5 is not supported and is read as 3 and 5; use a point for decimals.
What happens to text and other things that are not numbers?: They are left out and listed under the input, never silently dropped. For “12, 15, n/a, 18, abc” the calculator averages 12, 15 and 18 (15) and reports that “n/a” and “abc” were ignored. A currency symbol, a plus or minus sign and a trailing percent sign are accepted and dropped, so $5 reads as 5 and 20% as 20.
Why does the calculator show 0.3 for 0.1 + 0.2?: Most programs add decimals as binary floating-point numbers, where 0.1 + 0.2 is 0.30000000000000004. This calculator reads every number as an exact decimal and adds whole numbers, so the sum of 0.1 and 0.2 is 0.3 and their mean is 0.15. Results are shown in full when they end within 12 decimals and otherwise rounded to 6 decimals with a ≈ in front.
Is there a limit on how many numbers I can enter?: The calculator reads up to 200,000 numbers, each with up to 30 digits, and says so if more were pasted. Ten thousand numbers are worked out instantly in your browser, and nothing you enter is sent anywhere.

How it works

Every number you type is read as an exact decimal: its digits as a whole number and the count of digits after the point, so 0.1 is 1 over 10 and never the nearest binary fraction. All the numbers are brought to the same number of decimal places and added as whole numbers, which makes the sum, the mean (sum ÷ count), the median, the range, the minimum and the maximum exact fractions. The median is the middle of the sorted list, or the mean of the two middle values for an even count. The mode is every value that appears the most times, and “no mode” when no value repeats. The population variance is (n × Σx² − (Σx)²) ÷ n², and the sample variance divides the same numerator by n × (n − 1) instead; both are exact, and their square roots, the standard deviations, are the only approximate results, found to 12 decimals with integer arithmetic and then rounded for display. A weighted average is Σ(value × weight) ÷ Σ(weight). Display rule: a result that ends within 12 decimals is shown in full, anything longer is rounded half away from zero to 6 decimals and marked ≈, so you never see float noise and never lose a digit that was there. Reading rule: numbers are separated by spaces, tabs, new lines, semicolons or commas; a comma with no spaces around it between groups of exactly three digits (1,234 or 12,345,678.9) is a thousands separator, and any other comma separates numbers; a decimal comma is not supported. A plus or minus sign, one currency symbol, a trailing percent sign and E-notation (1.5e3) are accepted; anything else is ignored and listed. In a weighted list every line must be a value and a non-negative weight, and other lines are ignored and listed. Everything runs in your browser and nothing you type is sent anywhere.

Sources

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