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Facts and limits of this method
| Sample formula | Divisor n−1, matching Excel VAR.S |
|---|---|
| Population formula | Divisor n, matching Excel VAR.P |
| Units | Squared units of your data — minutes², roubles², kilograms² |
| Relationship | Variance is the square of the standard deviation; both are shown |
| Additivity | Variances of independent quantities add; standard deviations do not |
| Minimum rows | 2 for the sample formula |
When it misleads you
- Squared units make variance nearly impossible to interpret directly. A variance of 16 minutes² means a standard deviation of 4 minutes, and the second number is the one to put in a report.
- Because deviations are squared, a single outlier has an outsized effect — at four times the distance from the mean it contributes sixteen times the weight. Variance is even more sensitive to extreme values than the standard deviation is.
- The n−1 correction matters on small samples and becomes irrelevant on large ones. At 10 rows it changes the answer by about 11%; at 1000 rows by 0.1%.
- Like the standard deviation, variance assumes a roughly symmetric spread. On skewed data it is a technically correct number that describes nothing recognisable.
How it is calculated
Every value is compared to the mean, the difference is squared, and the squares are summed. Dividing that sum by n gives the population variance; dividing it by n−1 gives the sample variance.
The n−1 divisor exists because the mean was estimated from the same data the deviations are measured against. That makes the deviations systematically a little too small, and the smaller divisor compensates. This is Bessel’s correction, and it is why almost every statistics course and spreadsheet defaults to n−1.
The main practical reason to look at variance rather than the standard deviation is additivity: if two quantities are independent, the variance of their sum is the sum of their variances. Standard deviations cannot be added that way, which is why variance is the quantity that appears inside formulas even when it never appears in reports.
Both divisors are always computed and displayed together. The mismatch between a tool using n and a textbook using n−1 is the single most common source of "why do I get a different answer" — showing both removes the question.
Questions and answers
Should I report variance or standard deviation?
Standard deviation, in almost every case. It is in the same units as your data and can be compared to the mean directly. Variance is the working quantity behind the scenes.
Why does my variance look enormous?
Because it is in squared units. A delivery time varying by about 4 minutes gives a variance around 16, which sounds alarming until you take the square root.
n or n−1?
n−1 for a sample, n for a complete population. Sampled data is the normal case. Both are shown here so you can match whichever convention your source used.
Can variance be negative?
No. It is an average of squares, so it is always zero or positive. A variance of exactly zero means every value in the column is identical.
Is my file uploaded?
No. Everything is computed locally in your browser.