About this calculator
Paste or type a list of numbers and this calculator finds the mean (the average), the median (the middle value), the mode (the most common value), the range and the standard deviation, along with the working.
Separate the numbers with commas, spaces or new lines, so you can paste straight from a spreadsheet column. Both the sample and the population versions of standard deviation are shown, with a note on which to use.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
2, 4, 4, 4, 5, 5, 7, 9
- Mean (average)
- 5
- Median
- 4.5
- Mode
- 4
- Range
- 7
- Count
- 8
- Sum
- 40
- Smallest
- 2
- Largest
- 9
- Standard deviation (sample)
- 2.13809
- Standard deviation (population)
- 2
- Variance (sample)
- 4.571429
- Variance (population)
- 4
The 8 numbers have a mean of 5, a median of 4.5 and a range of 7.
Show the working
- Put the 8 numbers in order: 2, 4, 4, 4, 5, 5, 7, 9.
- Mean = sum ÷ count = 40 ÷ 8 = 5.
- Median: the two middle values are 4 and 5, and their average is 4.5.
- Mode: the most common value is 4 (appearing 3 times).
- Squared distances from the mean add up to 32.
- Sample standard deviation = √(32 ÷ (8 − 1)) = 2.13809. Population standard deviation = √(32 ÷ 8) = 2.
Test marks: 65, 72, 88, 72, 91
- Mean (average)
- 77.6
- Median
- 72
- Mode
- 72
- Range
- 26
- Count
- 5
- Sum
- 388
- Smallest
- 65
- Largest
- 91
- Standard deviation (sample)
- 11.28273
- Standard deviation (population)
- 10.091581
- Variance (sample)
- 127.3
- Variance (population)
- 101.84
The 5 numbers have a mean of 77.6, a median of 72 and a range of 26.
Show the working
- Put the 5 numbers in order: 65, 72, 72, 88, 91.
- Mean = sum ÷ count = 388 ÷ 5 = 77.6.
- Median: the middle value of 5 numbers is 72.
- Mode: the most common value is 72 (appearing 2 times).
- Squared distances from the mean add up to 509.2.
- Sample standard deviation = √(509.2 ÷ (5 − 1)) = 11.28273. Population standard deviation = √(509.2 ÷ 5) = 10.091581.
An outlier: 10, 12, 11, 13, 200
- Mean (average)
- 49.2
- Median
- 12
- Mode
- No mode (every value appears once)
- Range
- 190
- Count
- 5
- Sum
- 246
- Smallest
- 10
- Largest
- 200
- Standard deviation (sample)
- 84.307176
- Standard deviation (population)
- 75.406631
- Variance (sample)
- 7,107.7
- Variance (population)
- 5,686.16
The 5 numbers have a mean of 49.2, a median of 12 and a range of 190.
Show the working
- Put the 5 numbers in order: 10, 11, 12, 13, 200.
- Mean = sum ÷ count = 246 ÷ 5 = 49.2.
- Median: the middle value of 5 numbers is 12.
- Mode: no value appears more than once, so there is no mode.
- Squared distances from the mean add up to 28,430.8.
- Sample standard deviation = √(28,430.8 ÷ (5 − 1)) = 84.307176. Population standard deviation = √(28,430.8 ÷ 5) = 75.406631.
What each measure means
- Mean = the sum of all the numbers ÷ how many there are. It uses every value, so it's pulled by unusually large or small ones.
- Median = the middle value once the numbers are in order. With an even count, it's the average of the two middle values.
- Mode = the value that appears most often. There can be one mode, several, or none if every value appears once.
- Range = the largest value minus the smallest.
Mean or median?
The median is more reliable when there are outliers. In the last example, four numbers around 10 to 13 and one of 200, the mean is 49.2 (a figure that describes none of the numbers), but the median is 12, which is a fair picture of the typical value. Prices, salaries and house values are often reported as medians for this reason.
Standard deviation: sample or population?
Standard deviation measures how spread out the numbers are: the typical distance from the mean.
Population standard deviation divides the squared distances by n. Use it when your numbers are everything you care about, such as every test score in one class.
Sample standard deviation divides by n − 1. Use it when your numbers are a sample taken from a bigger group and you want to estimate the spread of that group. Dividing by n − 1 corrects for the fact that a sample tends to underestimate the true spread. If you're unsure, and your data is a sample of something larger, use the sample version.
How it's worked out
Take the numbers 2, 4, 4, 4, 5, 5, 7, 9. The sum is 40 and there are 8 numbers, so the mean is 5. Subtract the mean from each number, square each difference and add them up: the total is 32. The population standard deviation is √(32 ÷ 8) = 2, and the sample standard deviation is √(32 ÷ 7) = 2.138.
Frequently asked questions
How do I calculate the mean?
Add all the numbers together and divide by how many numbers there are. For 65, 72, 88, 72 and 91 the sum is 388 and there are 5 numbers, so the mean is 77.6.
How do I find the median?
Put the numbers in order and take the middle one. If there are two middle numbers, take their average. This calculator sorts them for you.
Can there be more than one mode?
Yes. If two or more values tie for most common, they're all modes. If every value appears just once, there is no mode.
What's the difference between sample and population standard deviation?
Population divides by n and is for complete data. Sample divides by n − 1 and is for a sample drawn from a larger group. The sample figure is slightly larger.
Why is there no sample standard deviation for one number?
With a single value there's no spread to measure, and dividing by n − 1 would mean dividing by zero.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.