Calculator Input
Enter grouped class intervals and frequencies. The tool sorts classes, builds cumulative frequency, locates the median class, and estimates the grouped median.
Example Data Table
| Marks Range | Frequency | Cumulative Frequency |
|---|---|---|
| 0 - 10 | 4 | 4 |
| 10 - 20 | 7 | 11 |
| 20 - 30 | 12 | 23 |
| 30 - 40 | 18 | 41 |
| 40 - 50 | 9 | 50 |
| 50 - 60 | 5 | 55 |
Formula Used
For grouped data, the median is estimated with this formula:
Median = L + [(N / 2 − CF) / f] × h
Here, L is the lower boundary of the median class. N is the total frequency. CF is the cumulative frequency before the median class. f is the frequency of the median class. h is the class width.
How to Use This Calculator
- Enter each class lower limit, upper limit, and frequency.
- Add more rows if your table has more class intervals.
- Use boundary correction when your grouped data needs class boundaries.
- Choose decimal places for cleaner results.
- Press the calculate button to view the median above the form.
- Use CSV or PDF buttons to export your result.
Understanding Median from Cumulative Frequency
What the Median Shows
The median is the middle value of a data set. In grouped statistics, exact individual values are often unavailable. We use class intervals and frequency counts instead. The median cumulative frequency method gives a reliable estimate for that middle position.
Why Cumulative Frequency Matters
Cumulative frequency shows how many observations are included up to each class. It grows as classes move from lower values to higher values. The median position is found at N divided by 2. The first class whose cumulative frequency reaches or passes this value is the median class.
Grouped Median Logic
After the median class is found, the formula estimates how far the median lies inside that class. It uses the previous cumulative frequency, class frequency, and class width. This interpolation assumes values are spread evenly inside the median class. That is why grouped medians are estimates, not exact raw medians.
When to Use This Tool
Use this calculator for marks, ages, income bands, survey ranges, production batches, and other grouped data. It is useful when data is already summarized in a frequency table. The graph helps compare class frequency with cumulative growth. The export buttons help save your calculation for homework, reports, audits, and classroom notes.
Tips for Better Accuracy
Always enter intervals in a consistent scale. Keep class widths equal when possible. Check that no frequency is missing. Use boundary correction only when class limits need continuous boundaries. Review the highlighted median class before using the final answer. A clean table gives a clearer and more dependable median estimate.
FAQs
1. What is median cumulative frequency?
It is a method used to estimate the median from grouped frequency data. It finds the middle position using cumulative totals.
2. What is the median class?
The median class is the first class interval whose cumulative frequency equals or exceeds N divided by 2.
3. Why is grouped median only an estimate?
Grouped data does not show every original value. The formula assumes values are evenly distributed inside the median class.
4. What does CF before mean?
CF before means the cumulative frequency before the median class. It counts all observations in lower classes.
5. What is class width?
Class width is the difference between the upper and lower limits of a class interval.
6. When should I use boundary correction?
Use boundary correction when class limits represent continuous intervals. For whole number classes, 0.5 is often used.
7. Can frequencies be decimal values?
Most frequency tables use whole counts. Decimal weights can work when the data represents weighted frequencies or survey weights.
8. Can I export my calculation?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a printable report.