Calculate an arithmetic or weighted average and see the median, population standard deviation, variance, quartiles, IQR and possible outlier flags in the same result.
| # | Value | Weight | Contribution (xΓw) | Note |
|---|---|---|---|---|
| No data has been calculated yet. | ||||
Arithmetic mean is the sum of all values divided by the number of values. Weighted mean is the sum of each value multiplied by its weight, divided by the total weight.
Standard deviation and variance treat the entered list as the entire population and therefore use population formulas. This calculator does not report sample standard deviation (nβ1).
In arithmetic mode, Q1 and Q3 use (nβ1) Γ q linear interpolation on sorted values. In weighted mode, the median and quartiles are the first sorted values at which the 25%, 50% and 75% cumulative-weight thresholds are reached.
When there are at least four values in arithmetic mode or four rows in weighted mode, the 1.5 Γ IQR rule is applied. Values outside the fences are flagged as possible outliers. A flag is a screening signal, not a context-free conclusion that the value is wrong.
In an arithmetic average, every value has equal influence. In a weighted average, each value is multiplied by its positive weight and total contribution is divided by total weight.
The calculator treats the entered list as the full population and reports population variance and population standard deviation. In weighted mode, the same measures incorporate positive weights.
With at least four values or weighted rows, the calculator applies the 1.5 Γ IQR rule. Arithmetic-mode quartiles use linear interpolation; weighted quartiles use cumulative-weight thresholds. The result is a screening flag, not a definitive outlier judgment.
Enter one value and one positive weight per line, separated by a semicolon. For example, 70;3 and 85.5;4 are valid rows.