Calculator Inputs
Use the controls below to enter grouped class intervals and frequencies. The interval input rows follow a 3-column large-screen, 2-column medium-screen, and 1-column mobile layout.
Example Data Table
This sample can be loaded directly with the example button above.
| Class interval | Frequency | Midpoint |
|---|---|---|
| 0–10 | 4 | 5 |
| 10–20 | 7 | 15 |
| 20–30 | 12 | 25 |
| 30–40 | 10 | 35 |
| 40–50 | 5 | 45 |
| 50–60 | 2 | 55 |
Formula Used
Midpoint of each class: m = (Lower limit + Upper limit) ÷ 2
Grouped mean: x̄ = Σ(fm) ÷ Σf
Population variance: σ² = Σ[f(m − x̄)²] ÷ Σf
Population standard deviation: σ = √σ²
Sample variance: s² = Σ[f(m − x̄)²] ÷ (Σf − 1)
Sample standard deviation: s = √s²
Because raw observations are unavailable, grouped measures use class midpoints as representative values. That makes the answer an estimate rather than an exact raw-data deviation.
How to Use This Calculator
- Enter a dataset label, optional units, and desired decimal places.
- Choose whether you want population or sample standard deviation reported.
- Add each class interval using lower limit, upper limit, and frequency.
- Keep upper limits larger than lower limits for every class.
- Click Calculate Standard Deviation to generate summary values, chart, and detailed working table.
- Use the CSV button for spreadsheet output and the PDF button for a printable report.
FAQs
1) What does grouped standard deviation measure?
It estimates how widely grouped observations spread around the grouped mean. Larger values show more dispersion across the class intervals.
2) Why does the calculator use midpoints?
Grouped tables do not contain every raw observation. Midpoints act as representative values for each class, making the deviation estimate possible.
3) When should I choose the population option?
Use population when the grouped table represents the full set you want to describe, such as all products, all students, or all recorded events.
4) When should I choose the sample option?
Use sample when your grouped table comes from only part of a larger population and you want an estimate adjusted for sampling.
5) Can frequencies be decimals?
Yes. The calculator accepts nonnegative numeric frequencies, which is useful for weighted grouped summaries or adjusted counts.
6) Why might grouped results differ from raw-data results?
Grouping compresses information. Replacing actual observations with class midpoints introduces approximation error, especially when classes are wide or uneven.
7) What does the coefficient of variation show?
It expresses standard deviation relative to the mean as a percentage. This helps compare variability across datasets with different scales.
8) What should I do if classes overlap?
Correct the intervals before calculation. Overlapping classes can distort grouped measures and make the frequency distribution difficult to interpret properly.