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Grouped Data Standard Deviation Calculator — result sheet
Estimate weighted mean and population or sample standard deviation from class midpoints and frequencies.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Weighted mean=Σfᵢmᵢ/N; population variance=Σfᵢ(mᵢ−mean)²/N; sample variance uses N−1.
Grouped data replace each class interval with its supplied midpoint, so the result is an estimate whose quality depends on the width and shape of the original classes.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Class midpoints — Comma-separated numeric class midpoints.
- Class frequencies — Comma-separated nonnegative integer frequencies matching the midpoints.
Worked example
| Input | Value |
|---|---|
| Class midpoints | 10, 20, 30, 40 |
| Class frequencies | 2, 5, 7, 3 |
Weighted mean ≈ 26.47; population standard deviation ≈ 9.037.
Assumptions and limits
- Each frequency is a nonnegative integer and each midpoint represents its class.
- Within-class variation is not known and is not reconstructed from the midpoint alone.
- The sample standard deviation uses N−1 while the population version uses N.
- Open-ended or highly uneven classes need a separately documented treatment.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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