Calculator Inputs
Use the responsive calculator grid below. Large screens show three columns, medium screens show two, and phones show one.
Example Data Table
This sample shows how grouped intervals and frequencies are organized before the calculator estimates the mean.
| Class Interval | Frequency | Midpoint | f×x |
|---|---|---|---|
| 0 - 10 | 4 | 5 | 20 |
| 10 - 20 | 7 | 15 | 105 |
| 20 - 30 | 10 | 25 | 250 |
| 30 - 40 | 6 | 35 | 210 |
| 40 - 50 | 3 | 45 | 135 |
| Total | 30 | 720 |
For this example, the grouped mean is 720 ÷ 30 = 24.
Formula Used
Grouped mean: x̄ = Σ(f × m) / Σf
Here, f is the class frequency and m is the midpoint of each class, found by (lower + upper) / 2.
Grouped variance: Σ[f(m - x̄)²] / N for a population, or Σ[f(m - x̄)²] / (N - 1) for a sample.
Grouped median: L + ((N/2 - cfb) / fm) × h, where L is the lower boundary of the median class, cfb is cumulative frequency before it, fm is its frequency, and h is class width.
Grouped mode: L + ((f1 - f0) / (2f1 - f0 - f2)) × h, using the modal class and adjacent class frequencies.
How to Use This Calculator
- Enter a dataset name so exported files remain easy to identify.
- Choose the number of decimal places you want in the output.
- Select population variance for full datasets or sample variance for sampled grouped data.
- Paste one class per line using low, high, frequency or low-high, frequency.
- Click Calculate Grouped Mean to show the result above the form.
- Review the summary cards, grouped table, quartiles, variability measures, and modal class.
- Download the calculated report as CSV or PDF when needed.
Frequently Asked Questions
1. What is a grouped mean?
A grouped mean estimates the average of binned data. It replaces raw observations with class midpoints, then weights each midpoint by its class frequency.
2. Why does the calculator use class midpoints?
Grouped data hides exact observations inside intervals. Midpoints provide a practical representative value for each class, making average and dispersion calculations possible.
3. Can I use unequal class widths?
Yes. The grouped mean still works with unequal widths because each class midpoint is weighted by its own frequency. Median and mode estimates also use each class width directly.
4. Should I choose population or sample variance?
Choose population when your grouped table contains the complete dataset. Choose sample when the grouped table summarizes a sample drawn from a larger population.
5. Does this support open-ended intervals?
No. Open-ended classes lack one bound, so a midpoint cannot be determined reliably. Add a usable lower and upper limit before calculating.
6. What export formats are included?
The calculator can download a CSV file for spreadsheet work and a PDF report for sharing, archiving, or attaching to project documentation.
7. Is the grouped mean exact?
It is an estimate, not the exact raw-data average. Accuracy depends on how tightly the class intervals represent the original observations.
8. What input format is accepted?
Enter one class per line. Use either low, high, frequency or low-high, frequency. Commas, semicolons, tabs, and vertical bars are accepted separators.