Mean, Median and Mode Calculator
Paste a list of numbers. Get the mean, median, mode, range and standard deviation.
How it works
Separate numbers with spaces, commas or new lines, up to 1,000 of them. You get standard deviation both ways: population when you have the whole group, and sample when your data is part of a larger group.
Example
Find the mean, median and mode of 12, 7, 3, 7, 9, 15, 7, 10.
Mean 8.75 · Median 8
- Mode
- 7
- Range
- 12
- Count
- 8
- Sum
- 70
- Std dev (population)
- 3.4187
- Std dev (sample)
- 3.6547
Steps
- In order: 3, 7, 7, 7, 9, 10, 12, 15.
- Mean: 70 ÷ 8 = 35/4 ≈ 8.75.
- Median: with 8 values, average numbers 4 and 5: (7 + 9) / 2 = 8.
- Mode: 7 shows up most (3 times).
- Range: 15 − 3 = 12.
- Squared distances from the mean add up to 93.5. Population: √(93.5 / 8) = 3.4187. Sample: √(93.5 / 7) = 3.6547.
More examples
Find the mean and median of 20, 22, 25, 24, 200.
Mean 58.2 · Median 24
- Mode
- None
- Range
- 180
- Count
- 5
- Sum
- 291
- Std dev (population)
- 70.9208
- Std dev (sample)
- 79.2919
Steps
- In order: 20, 22, 24, 25, 200.
- Mean: 291 ÷ 5 = 291/5 ≈ 58.2.
- Median: with 5 values, it’s value number 3: 24.
- Mode: no value repeats, so there is no mode.
- Range: 200 − 20 = 180.
- Squared distances from the mean add up to 25148.8. Population: √(25148.8 / 5) = 70.9208. Sample: √(25148.8 / 4) = 79.2919.
Find the mean, median and mode of 88, 92, 79, 92, 85, 64.
Mean 83.3333 · Median 86.5
- Mode
- 92
- Range
- 28
- Count
- 6
- Sum
- 500
- Std dev (population)
- 9.724
- Std dev (sample)
- 10.6521
Steps
- In order: 64, 79, 85, 88, 92, 92.
- Mean: 500 ÷ 6 = 250/3 ≈ 83.3333.
- Median: with 6 values, average numbers 3 and 4: (85 + 88) / 2 = 173/2.
- Mode: 92 shows up most (2 times).
- Range: 92 − 64 = 28.
- Squared distances from the mean add up to 567.3333. Population: √(567.3333 / 6) = 9.724. Sample: √(567.3333 / 5) = 10.6521.
Common mistake
Sort the list before finding the median. With an even count, average the two middle values.
Questions
Mean or median: which should I use?
The median when there are outliers. In 20, 22, 25, 24, 200 the mean is 58.2, but the median, 24, is closer to most of the data.
Can a list have no mode, or two?
Yes. If every value appears once there is no mode. If two values tie for most often, both are modes.
Population or sample standard deviation?
Use population when the list is the whole group, and sample when it is part of a bigger group. Sample divides by n − 1, so it comes out a little larger.