Median Formula for Grouped Data Calculator

Compute grouped medians from intervals and frequencies. Review cumulative steps, charts, exports, and class boundaries. Clear outputs support faster statistical decisions for every dataset.

Calculator

Enter grouped intervals and frequencies. The form uses three columns on large screens, two on medium screens, and one on mobile.

Lower Limit Upper Limit Frequency Row
Example Data Table

This example dataset is also used by the quick-fill button above.

Class Interval Frequency Cumulative Frequency
0 - 1044
10 - 20711
20 - 301122
30 - 401537
40 - 50946
50 - 60450
Formula Used

Grouped median formula:

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 = width of the median class

When intervals are inclusive whole numbers, the calculator converts limits to boundaries by subtracting 0.5 from each lower limit and adding 0.5 to each upper limit.

How to Use This Calculator
  1. Enter a title, unit label, and decimal preference.
  2. Select whether your intervals are continuous or inclusive.
  3. Fill each class interval with its frequency value.
  4. Add or remove rows as needed.
  5. Press Calculate Median to view the grouped median.
  6. Review the highlighted median class and interpolation details.
  7. Use the CSV or PDF buttons to export the output.
  8. Inspect the Plotly graph for frequency and cumulative trends.
FAQs

1. What is grouped data?

Grouped data combines observations into class intervals instead of listing every raw value. This makes large datasets easier to summarize and compare.

2. Why does the calculator use N/2?

The median divides ordered data into two equal halves. For grouped distributions, N/2 identifies the median position before interpolation inside the median class.

3. What is the median class?

The median class is the first class whose cumulative frequency equals or exceeds N/2. It contains the estimated median value.

4. Why are class boundaries important?

Boundaries create continuous class ranges for interpolation. They are especially useful when intervals are written as inclusive whole-number classes, such as 10–19 or 20–29.

5. Can this handle unequal class widths?

Yes. The formula uses the width of the median class. The page also warns you when widths differ across intervals.

6. What happens if intervals overlap?

Overlapping classes break the grouped median logic. The calculator blocks those entries and asks for corrected intervals before computing the result.

7. What does the chart show?

The Plotly graph displays class frequencies as bars and cumulative frequencies as a line. This helps you spot where the median position falls.

8. Is the grouped median exact?

It is an estimate based on interpolation within the median class. Raw ungrouped data can produce a more exact median.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.