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Statistics · Descriptive statistics

Weighted Descriptive Statistics Calculator

Summarize values with positive frequencies or importance weights, including weighted center, spread, quantiles, and effective sample size.

Statistics · Descriptive statistics

Enter your statistical inputs

Private in-browser calculation · explicit assumptions

Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. 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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