Median Calculator for Grouped Data

Example Data Table

Formula Used

Median = L + [(N / 2 - CF) / f] × h

L means the lower boundary of the median class. N means total frequency. CF means cumulative frequency before the median class. f means frequency of the median class. h means class width.

How to Use This Calculator

1. Enter each class lower limit, upper limit, and frequency.
2. Use ordered intervals for better results.
3. Select a continuity correction when using inclusive integer classes.
4. Enter a custom width only when your table requires it.
5. Click the calculate button.
6. Review the median class, cumulative totals, and final answer.
7. Use CSV or PDF export for saving the result.

Grouped Data Median Guide

What Grouped Data Means

Grouped data appears when values are collected into class intervals. It is common in surveys, exams, income studies, production records, and grouped reports. The median is the center value. It divides the ordered distribution into two equal parts. With raw data, you can sort values directly. With grouped data, the exact values are hidden inside each interval. So the median must be estimated with interpolation.

How the Median Class Is Found

This calculator follows the standard grouped median method. It first totals all frequencies. Then it finds one half of the total frequency. Next, it builds cumulative frequency row by row. The class where cumulative frequency first reaches or passes half of the total is the median class. That class holds the estimated middle position.

How the Formula Works

The formula uses four important values. 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. The result is L plus the remaining proportion of the class width. This method assumes values are spread evenly across the median class.

Advanced Options

Advanced options help you handle different table styles. You can use exact limits for continuous data. You can also apply a continuity correction for inclusive integer classes. For example, 10 to 19 becomes 9.5 to 19.5. That gives a class width of 10. You may also enter a custom class width when your table needs a fixed interval size.

Accuracy Tips

A good grouped median table should have ordered intervals. Class limits should not overlap. Frequencies should be zero or positive. The median class must have a positive frequency. If rows are missing or unordered, the estimate may be misleading. Always review the cumulative table before using the answer.

Exporting Results

Use the export tools when you need records. The CSV button saves the computed rows. The PDF button creates a report with inputs, formula values, and the final median. These files help with assignments, audits, lessons, and statistical notes. The calculator is an estimator, not a replacement for raw data. When raw observations are available, compute the exact median from those values. When only a frequency table is available, grouped interpolation gives a practical and accepted estimate.

FAQs

What is the median for grouped data?

It is an estimated center value from a frequency table. Since exact raw values are not listed, the calculator uses the median class and interpolation to estimate the middle point.

What is the median class?

The median class is the class interval where cumulative frequency first reaches or passes N / 2. It contains the estimated middle observation of the grouped distribution.

Why is interpolation used?

Interpolation estimates where the middle value lies inside the median class. It assumes values are evenly distributed across that class interval.

What does CF mean in the formula?

CF means cumulative frequency before the median class. It shows how many observations are counted before the class containing the median position.

When should I use continuity correction?

Use 0.5 correction for inclusive integer classes like 10 to 19. It changes class limits into boundaries, such as 9.5 to 19.5.

Can frequencies include decimals?

Yes, the calculator accepts decimal frequencies. However, most grouped frequency tables use whole numbers because frequencies usually count observations.

Why should classes be ordered?

Ordered classes are required for correct cumulative frequency. If intervals are mixed or overlapping, the median class may be selected incorrectly.

Is this median exact?

It is an estimate. Grouped data hides exact values inside intervals, so the result depends on the standard assumption of even spread within the median class.