Grouped Median Calculator

Enter grouped data

Enter one class interval per line in this format: lower limit, upper limit, frequency. Example: 10,20,7

Class intervals and frequencies

Decimal places Manual boundary correction

Apply automatic continuity correction of 0.5

Tips

Keep intervals in ascending order.
Use equal widths for cleaner interpretation.
Use frequencies greater than or equal to zero.

What this tool returns

Median class detection
Cumulative frequency table
Lower and upper class boundaries
Worked grouped median formula values
CSV and PDF export options
Interactive Plotly graph

Example data table

Class Interval	Frequency	Cumulative Frequency
0 - 10	5	5
10 - 20	9	14
20 - 30	12	26
30 - 40	8	34
40 - 50	6	40

In this example, N = 40 and N/2 = 20. The cumulative frequency first exceeds 20 in the 20 - 30 class, so that is the median class.

Formula used

The grouped median estimates the center of a frequency distribution when raw observations are not listed individually. It uses the lower class boundary of the median class, the total frequency, the cumulative frequency before the median class, the frequency of the median class, and the class width.

Median = L + [ ((N / 2) - cf) / f ] × h

L = lower boundary of the median class

N = total frequency

cf = cumulative frequency before the median class

f = frequency of the median class

h = class width

How to use this calculator

Enter each class interval and its frequency on a new line.
Use the format: lower limit, upper limit, frequency.
Choose the number of decimal places for the final output.
Enter a manual boundary correction or enable automatic 0.5 correction.
Click Calculate Grouped Median to generate the result.
Review the median class, worked formula, cumulative table, and graph.
Use the CSV or PDF buttons to export the result.

Frequently asked questions

1. What is a grouped median?

A grouped median is the estimated middle value of a frequency distribution arranged into class intervals. It is useful when exact raw values are unavailable but grouped counts are provided.

2. How is the median class identified?

The median class is the first class whose cumulative frequency is equal to or greater than half of the total frequency. That class contains the median estimate.

3. Why does the formula use class boundaries?

Class boundaries make interpolation smoother, especially for continuous grouped data. They help estimate where the true median lies inside the median class.

4. When should I use continuity correction?

Use continuity correction when class limits represent rounded whole-number intervals, such as 10–19 and 20–29. A 0.5 correction often improves boundary-based interpolation.

5. Can class widths be unequal?

Yes, the calculator still works if widths differ. However, interpretation is cleaner when the class structure is consistent and carefully checked for gaps or overlaps.

6. What happens if a frequency is zero?

Zero frequencies are allowed in non-median classes. The median class itself must have positive frequency, or the grouped interpolation step cannot be completed correctly.

7. Does this calculator show cumulative frequencies?

Yes. It builds a cumulative frequency table, highlights the median class, and shows each value needed in the grouped median formula.

8. Can I export my results?

Yes. After calculation, you can export the computed table as CSV or generate a PDF summary for reporting, teaching, or revision purposes.