- Mean
- 5
- Median
- 4.5
- Mode
- 4
- Sample standard deviation
- 2.14
- Sample variance
- 4.57
- Population standard deviation
- 2
- Population variance
- 4
- Count
- 8
- Sum
- 40
- Minimum
- 2
- Maximum
- 9
- Range
- 7
- Sum of squares
- 232
- Geometric mean
- 4.6
How it works
Group averages need group sizes
Ten observations averaging 20 and thirty averaging 40 combine to a mean of 35, not 30. To use this unweighted list tool, enter the original observations rather than just the two group averages.
Choosing what an average should describe
For the values 10, 12, 14, and 100, the sum is 136 and the arithmetic mean is 34. The median is 13, halfway between the two middle values after sorting. The large value of 100 pulls the mean upward, which is why reporting only the average can hide the shape of the data. Include each observation once and use consistent units. For course grades or other weighted observations, use a tool that accepts weights rather than treating every value equally.
Dataset summary: formula and assumptions
Mean = Σx / n; population variance = Σ(x − mean)² / n; sample variance uses n − 1.
The mean uses every value. The median is the middle of the sorted dataset. Sample variance corrects for estimating a population from a sample.
Worked example
Using the Dataset summary example:
- Numbers
- 2, 4, 4, 4, 5, 5, 7, 9
Mean = Σx / n; population variance = Σ(x − mean)² / n; sample variance uses n − 1.
Example result
Mean: 5
Median: 4.5
Mode: 4
Sample standard deviation: 2.14
Sample variance: 4.57
Population standard deviation: 2
Population variance: 4
Count: 8
Sum: 40
Minimum: 2
Maximum: 9
Range: 7
Sum of squares: 232
Geometric mean: 4.6
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
- OpenStax: Algebra and Trigonometry (opens in a new tab)
- NIST statistical methods handbook (opens in a new tab)
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Can one unusually large value change the average?
Yes. The mean uses every value, so an extreme value can shift it substantially. Comparing the median helps reveal that effect.
Is this a weighted average?
No. Each entered value contributes equally. A weighted mean requires explicit weights and a different calculation.
Prepared by Finflo. See our methodology and editorial policy.