Weighted Mean Calculator
Compute weighted mean from numbers and weights. Add pairs, calculate instantly, view formula, see steps, and clear or load examples.
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Helping Notes
Enter each data value and its weight. Weights may be raw numbers or percentages; the calculator normalizes by their sum. :contentReference[oaicite:1]{index=1}
Leave unused rows empty or remove them. All pairs must be numeric; negative weights are not typical and will be flagged.
Results
Weighted Mean \(\bar{x}\)
Weighted Sum \(\sum w_i x_i\)
Sum of Weights \(\sum w_i\)
What Is a Weighted Mean Calculator?
A Weighted Mean Calculator finds the average of numbers when each value carries an importance or frequency indicated by a weight. Unlike the simple (unweighted) average that treats every observation equally, the weighted mean gives larger influence to observations with higher weights and less to those with smaller weights. This is essential in survey analysis (respondent weights), grading systems (assignment categories), finance (portfolio returns), and operations (service-level aggregation). The calculator accepts raw values and any nonnegative weights, supports either raw weights that need normalization or probability weights that already sum to one, and returns the weighted mean together with useful diagnostics. Clear, render‑ready formulas show exactly how the result is computed, so you can check assumptions and reuse the steps in spreadsheets or reports.
About the Weighted Mean Calculator
The engine computes the core ratio of the weighted sum to the total weight, handles missing values by filtering pairs with undefined entries, and warns when the total weight is zero. If you pass weights that sum to one, it skips normalization automatically; otherwise, it normalizes internally for transparency. Advanced helpers include effective sample size for unequal weights and optional weighted variance for error bars. You can paste columns, use category totals (group means with counts), or mix decimals and integers—everything is standardized before calculation. The output shows the weighted mean, total weight, normalization status, and checks like the unweighted mean for comparison, helping you decide whether weighting materially changes conclusions.
Weighted mean (raw weights):
Normalized weights:
Probability weights (sum to 1):
Effective sample size (diagnostic):
Optional weighted variance:
Group aggregation:
How to Use This Weighted Mean Calculator
- Enter values xi and corresponding nonnegative weights wi. Use 1 for equal weighting if you lack weights.
- Choose whether your weights already sum to one. If not, the tool normalizes automatically for clarity.
- Enable optional diagnostics to see effective sample size and weighted variance.
- Compute. Copy the weighted mean and any diagnostics into your worksheet or report.
Examples
- Grades: Quiz 80 (20%), Midterm 70 (30%), Final 90 (50%) → .
- Portfolio return: Asset A 5% (weight 0.6), B 2% (0.3), C −1% (0.1) → 3.5%.
- Group means: Dept A mean 72 (n=30), Dept B 80 (n=10) → .
- Unequal weights diagnostic: w = [5,1,1], x = [10,0,0] → .
Formula Snippets Ready for Rendering
FAQs
What’s the difference between weighted and unweighted mean?
The unweighted mean treats all observations equally; the weighted mean scales each value by its weight before averaging.
Do my weights need to sum to one?
No. The calculator will normalize raw weights internally; if they already sum to one, results are identical.
Can weights be zero or negative?
Zero removes an item from influence. Negative weights are uncommon and generally not recommended outside specialized estimators.
How do I choose weights?
Use frequencies, proportions, reliability scores, time on task, or economic size—whatever reflects each observation’s importance.
What if I have group means and counts?
Multiply each group mean by its count and divide by the total count (see the group aggregation formula above).
How does missing data affect results?
Pairs with missing value or weight are ignored. Consider imputation if missingness is systematic.
What is effective sample size?
A diagnostic showing how unequal weights reduce information relative to a simple random sample of the same size.
Is there a weighted median?
Yes—order values by size and accumulate weights until you pass 50%. It’s more robust to outliers than the mean.
Can I compute a weighted variance?
Yes; enable the option to see the formula and result for dispersion around the weighted mean.