Enter Grouped Data
Use class intervals and frequencies to analyze a grouped distribution.
Example Data Table
This sample grouped dataset shows how class intervals and frequencies can be organized before calculation.
| Class Interval | Frequency | Cumulative Frequency | Midpoint |
|---|---|---|---|
| 10 - 20 | 4 | 4 | 15 |
| 20 - 30 | 7 | 11 | 25 |
| 30 - 40 | 11 | 22 | 35 |
| 40 - 50 | 9 | 31 | 45 |
| 50 - 60 | 5 | 36 | 55 |
| 60 - 70 | 2 | 38 | 65 |
Formula Used
Grouped frequency analysis uses class intervals, midpoints, and frequencies.
Class midpoint: Midpoint = (Lower Boundary + Upper Boundary) ÷ 2
Mean: Mean = Σ(f × x) ÷ Σf
Median: Median = L + [((N ÷ 2) − c.f.) ÷ f] × h
Mode: Mode = L + [(f1 − f0) ÷ (2f1 − f0 − f2)] × h
Population variance: Variance = Σ[f(x − x̄)²] ÷ N
Population standard deviation: Standard Deviation = √Variance
How to Use This Calculator
- Enter an optional dataset name for your report.
- Select how many decimal places you want displayed.
- Type each class interval using lower and upper boundaries.
- Enter the frequency for every class interval.
- Add more rows if your grouped table needs them.
- Click the calculate button to generate the distribution.
- Review totals, grouped measures, cumulative frequencies, and chart output.
- Download the finished table as CSV or PDF.
Frequently Asked Questions
1) What does this calculator measure?
It analyzes grouped frequency data using class intervals and frequencies. It also estimates mean, median, mode, variance, standard deviation, cumulative frequency, percentages, and midpoint totals.
2) Can I use decimal class boundaries?
Yes. The calculator accepts decimal lower and upper boundaries. This helps when your grouped data uses precise class intervals, measurement bands, or continuous ranges.
3) Why are midpoints important?
Midpoints represent each class interval with one central value. They are used to estimate grouped statistics, especially the grouped mean and variance.
4) What is cumulative frequency?
Cumulative frequency is the running total of frequencies from the first class onward. It helps identify median position, distribution buildup, and class coverage over time.
5) Does grouped mode always match an exact value?
No. Grouped mode is an estimate based on the modal class and neighboring class frequencies. It is strongest when class widths are consistent and data is well grouped.
6) What happens if my class widths differ?
The calculator still returns results. However, grouped mode interpretation becomes less reliable. Mean, totals, cumulative frequencies, and midpoint-based measures still remain useful.
7) Can I export the finished results?
Yes. Use the CSV button for spreadsheets and the PDF button for printable reports. Both options export the current calculated summary and detailed distribution table.
8) Is this suitable for exam statistics or business reports?
Yes. It works well for grouped marks, age bands, income classes, sales ranges, production intervals, survey groups, and other summarized statistical datasets.