Grouped data calculator form
Use the responsive class entry rows below. Large screens show three inputs per row, smaller screens show two, and mobile shows one.
Example grouped data table
This sample demonstrates five class intervals with a complete frequency distribution.
| Lower Limit | Upper Limit | Frequency |
|---|---|---|
| 0 | 9 | 4 |
| 10 | 19 | 7 |
| 20 | 29 | 10 |
| 30 | 39 | 6 |
| 40 | 49 | 3 |
Formula used
The calculator uses class midpoints and grouped interpolation formulas.
Mean
Mean = Σ(f × x) / Σf
Variance
Population variance = Σ[f(x - x̄)^2] / N
Sample variance = Σ[f(x - x̄)^2] / (N - 1)
Median
Median = L + ((N/2 - cfb) / fm) × h
Mode
Mode = L + ((f1 - f0) / (2f1 - f0 - f2)) × h
Quartiles and variation
Q1 = L + ((N/4 - cfb) / f) × h
Q3 = L + (((3N)/4 - cfb) / f) × h
Coefficient of variation = (SD / Mean) × 100
How to use this calculator
- Enter each grouped class using a lower limit, upper limit, and frequency.
- Choose inclusive or exclusive intervals according to your dataset.
- Set a boundary correction when inclusive limits need continuous class boundaries.
- Select population or sample variance based on your statistical goal.
- Adjust decimal precision for cleaner summaries and exported tables.
- Click the calculate button to show results above the form.
- Review the chart, summary table, and processed class details.
- Export the output as CSV or PDF for reporting.
Frequently asked questions
1. What does a grouped data calculator do?
It summarizes frequency distributions built from class intervals instead of raw observations. The calculator estimates mean, median, mode, quartiles, spread, cumulative frequencies, and other measures using grouped-data formulas.
2. When should I use inclusive intervals?
Use inclusive intervals when both class limits belong to the class, such as 10–19 and 20–29. Many school and exam tables use this style and often need boundary correction for interpolation.
3. Why is boundary correction important?
Boundary correction converts inclusive classes into continuous boundaries. That improves estimates for median, mode, and quartiles because grouped interpolation works best when each class behaves like a continuous interval.
4. What is the difference between population and sample variance?
Population variance divides by total frequency, while sample variance divides by total frequency minus one. Choose sample variance when the grouped table represents a sample from a larger population.
5. Are the results exact for grouped data?
Grouped statistics are estimates because each class is represented by its midpoint and interpolation assumptions. They are very useful for summaries, but raw ungrouped data remains more exact whenever available.
6. Can I use unequal class widths?
Yes. The calculator reads each row independently and uses the class width of the relevant interval in interpolation. Review results carefully because unequal widths can change interpretation, especially for visual comparisons.
7. What does the Plotly chart show?
The chart combines class frequencies with cumulative frequency. That helps you inspect distribution shape, concentration, and growth across intervals without manually drawing separate histograms or ogives.
8. What is included in the CSV and PDF downloads?
The CSV file contains summary metrics and processed class rows. The PDF includes the results overview tables and the chart, making it suitable for assignments, reports, and quick documentation.