How this calculation works
The mean uses all values; the median is the middle of the sorted data. Standard deviation is the square root of variance. Choose population when the data are the entire group, or sample when estimating population spread from a sample.
Mean = sum ÷ n; variance = sum of squared deviations ÷ n (or n − 1)A worked example
For 2, 4, 4, 4, 5, 5, 7, 9, the mean and median are 5. Population variance is 4 and standard deviation is 2.
Good to know
Numbers are equally weighted. This summary does not establish a distribution, independence or statistical significance. Large-magnitude numbers can lose precision in browser arithmetic.
The same average can hide very different data
The sets 4, 5, 6 and 0, 5, 10 both have a mean of 5 and a median of 5. The second set is much more spread out. An average alone cannot tell you how tightly the observations cluster, which is why the tool also reports variance, standard deviation and extremes.
An outlier can move the mean more strongly than the median. Replace the 6 in the first set with 600: the mean rises dramatically, while the median stays 5. Neither measure is automatically wrong; they summarize different features.
Choose population or sample deliberately
Population variance divides by n. Sample variance uses n − 1 when estimating population variance from a sample under the usual assumptions. That change matters most for small datasets; a single observation cannot supply a sample variance.
Standard deviation has the same units as the original numbers, while variance has squared units. A standard deviation in centimetres can be compared with a height measurement; variance in square centimetres needs a different interpretation.
A few questions, answered
Does the tool remove outliers?
No. Every entered number is retained with equal weight. Investigate unusual values rather than silently deleting them.
Can I enter scientific notation?
Yes. For example, 1e3 represents 1,000. Values must be finite real numbers.