- 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
Range can miss changes in the middle
The lists 0,5,5,10 and 0,0,10,10 share mean 5, median 5 and range 10. Their observations cluster differently. Compare the actual values and frequencies before treating matching summaries as equivalent datasets.
Reading the center and spread of a dataset
The mean, median, mode, and range answer different questions about the same data. The mode identifies repeated values, while the range depends only on the smallest and largest entries. Two datasets can share a mean and still have very different distributions. Review the original values as well as these summaries, especially when the list contains outliers or repeated measurements.
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 can the mean and median be different?
The mean uses the sum of all values; the median uses their sorted middle. Skewed or extreme values can separate them.
Can a dataset have more than one mode?
Yes. Several values can tie for the highest frequency. A mode describes frequency, not necessarily the center of the data.
Prepared by Finflo. See our methodology and editorial policy.