Calculated Result
The median estimate appears here after submission and stays above the form for review.
| Class Interval | Frequency | Cumulative Frequency | Class Width | Median Class |
|---|
Calculator Input
Enter grouped continuous class intervals and frequencies. The tool will sort rows, build cumulative totals, and interpolate the median.
Example Data Table
| Class Interval | Frequency | Cumulative Frequency |
|---|---|---|
| 0 - 10 | 4 | 4 |
| 10 - 20 | 7 | 11 |
| 20 - 30 | 12 | 23 |
| 30 - 40 | 9 | 32 |
| 40 - 50 | 3 | 35 |
For this example, total frequency is 35, so the median position is 17.5. The median class is 20 - 30, giving an estimated median of 25.4167.
Formula Used
Grouped-data median formula:
Median = L + ((N / 2 - cf) / f) × h
Where L is the lower boundary of the median class, N is total frequency, cf is cumulative frequency before the median class, f is the median class frequency, and h is the median class width.
The calculator first sorts all intervals, sums frequencies, identifies the class containing N / 2, then performs linear interpolation inside that class.
How to Use This Calculator
- Enter each lower bound, upper bound, and frequency.
- Add more class rows with the add button.
- Keep intervals ordered and nonoverlapping whenever possible.
- Set the desired decimal precision for the result.
- Press the calculation button to compute the median.
- Review the median class, interpolation details, and processed table.
- Export the output as CSV or PDF when needed.
Frequently Asked Questions
1) What data should I enter?
Enter class lower bounds, upper bounds, and frequencies for a grouped continuous distribution. The tool sorts rows, builds cumulative frequency, identifies the median class, and interpolates the median within that class.
2) Can I use unequal class widths?
Yes. The calculator uses the width of the detected median class during interpolation. Still, large width changes can make grouped summaries harder to interpret, so consistent intervals remain preferable.
3) Should classes overlap?
No. Intervals should be ordered and nonoverlapping. Small gaps may reflect different boundary conventions, but overlapping classes can distort cumulative frequency and place the median in the wrong class.
4) Why does this differ from a raw-data median?
This tool estimates the median from grouped data, not individual observations. Grouping compresses detail, so the interpolated value is an approximation based on class width, frequency, and cumulative position.
5) What if some frequencies are zero?
Zero frequencies are allowed, but the median class itself must have positive frequency. If several middle classes contain zero, regroup the distribution so the central position falls inside a meaningful interval.
6) How is the median class chosen?
The tool finds the first class whose cumulative frequency reaches or exceeds half the total frequency. That interval contains the median position used in interpolation.
7) What happens after sorting?
Rows are automatically sorted by lower bound before calculation. This helps correct entry order, but you should still review intervals carefully to avoid overlap, gaps, or typing mistakes.
8) Can I export results?
Yes. Download a CSV summary for spreadsheets or a PDF report for sharing. The export includes key median statistics and the processed grouped-frequency table.