- 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
Changing units changes spread predictably
Multiplying every observation by 10 multiplies standard deviation by 10 and variance by 100. Adding 10 to every observation changes the mean but leaves both spread measures unchanged, because distances from the mean stay the same.
Population and sample standard deviation
For 2, 4, and 6, the mean is 4. Squared deviations are 4, 0, and 4, totaling 8. Treating the list as the whole population gives variance 8 ÷ 3 and standard deviation about 1.63. Treating it as a sample gives variance 8 ÷ 2 = 4 and standard deviation 2. Choose the interpretation that matches your data, not the smaller answer. Standard deviation uses the original unit; variance uses its square.
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
Why is sample standard deviation usually larger?
Sample variance divides squared deviations by n − 1 instead of n. Taking the square root preserves that difference.
Does standard deviation use the same units as my data?
Yes. Variance uses squared units, while standard deviation takes the square root and returns to the original unit.
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