Understand the statistic
What the weighted descriptive statistics calculator tells you
Finding a representative center. A measure of center compresses many observations into a useful reference point. The right center depends on the data shape, weighting rule, and the question being asked.
1Start with the entered observations2Apply the stated center or weighting rule3Compare the result with the original spread
Calculation rule
Weighted mean = Σwᵢxᵢ/Σwᵢ; weighted population variance = Σwᵢ(xᵢ−μw)²/Σwᵢ.
The formula is applied only to the observations and options you enter. No population, distribution, or sampling process is inferred automatically.
How to read the answer
Frequency weights represent replicated observations; sampling or importance weights represent unequal influence. Those meanings are not interchangeable for inference.
Important: Frequency weights must be positive whole numbers and their sum is the replicated observation count. Sampling or importance weights may be positive decimals; only that mode reports Kish effective sample size. Weighted quartiles use the inverse weighted empirical CDF.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the weighted descriptive statistics calculator works
Weighted mean = Σwᵢxᵢ/Σwᵢ; weighted population variance = Σwᵢ(xᵢ−μw)²/Σwᵢ.
Frequency weights represent replicated observations; sampling or importance weights represent unequal influence. Those meanings are not interchangeable for inference.
Worked example
Weighted Descriptive Statistics example
Values 10 and 20 with weights 1 and 3 have a weighted mean of 17.5 rather than the unweighted mean of 15.
Weighted mean = Σwᵢxᵢ/Σwᵢ; weighted population variance = Σwᵢ(xᵢ−μw)²/Σwᵢ.
Supported inputs
Precision and limits
Model and design
Frequency weights must be positive whole numbers and their sum is the replicated observation count. Sampling or importance weights may be positive decimals; only that mode reports Kish effective sample size. Weighted quartiles use the inverse weighted empirical CDF.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
Frequency weights represent replicated observations; sampling or importance weights represent unequal influence. Those meanings are not interchangeable for inference.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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