Estimate medians from grouped intervals with clear cumulative checks. Add rows, validate inputs, and export reports. Built for practical data workflows daily.
| Class Interval | Frequency |
|---|---|
| 0–10 | 3 |
| 10–20 | 7 |
| 20–30 | 12 |
| 30–40 | 8 |
| 40–50 | 5 |
For grouped data, the median is estimated using the median class and cumulative frequencies:
Grouped frequency tables appear in sensor binning, A/B logs, and survey bands where raw values are unavailable or too large to store. This calculator accepts class limits and frequencies, then builds cumulative totals to locate the median class where the running count crosses N/2.
In production pipelines, grouped summaries often come from histogram aggregations, privacy-preserving telemetry, or edge devices that transmit counts instead of raw samples. Because only totals are known, percentile estimates must rely on within-bin interpolation rather than sorting individual observations.
For a dataset of N observations, the median marks the 50th percentile. With grouped data, the exact middle value is estimated by assuming values are uniformly distributed within the median class. That assumption is reasonable when intervals are narrow and measurements are continuous.
The tool reports the median class, cumulative frequency before it (cf_prev), class width (h), and the chosen lower reference (L). Using these, it computes Median = L + ((N/2 − cf_prev) / f_m) × h, where f_m is the median class frequency.
When classes are discrete such as 10–19, 20–29, use boundaries by subtracting an adjustment (commonly 0.5) from the lower limit. This converts limits to continuous boundaries and reduces rounding bias. For already-continuous classes like 0–10, limits mode is typically sufficient.
Data quality controls matter. Overlapping intervals bias the cumulative curve, while zero frequency in the median class makes the estimate undefined. Keep intervals ordered, use consistent units, and verify that boundaries match how classes were constructed in your source system.
Exports support reproducible analysis. CSV captures inputs and the cumulative table for versioning, while PDF provides a shareable report for stakeholders. Pair the median with grouped mean and dispersion measures to summarize distributions across time windows, cohorts, or model segments.
In data science reporting, the grouped median is robust to extreme tails compared with the mean, making it useful for latency, spend, and duration metrics. Track it alongside sample size changes; a stable median with shrinking N may still indicate reduced coverage or filtering.
Use narrow, consistent bins when possible, and document interval definitions so future teams can reproduce the exact same median.
The grouped median is an estimate of the middle value when data is available only as class intervals with frequencies. It interpolates within the median class using cumulative frequency position.
Use boundary mode for discrete class limits like 10–19 or 20–29. Applying an adjustment (often 0.5) converts limits into continuous boundaries and reduces rounding bias.
Cumulative frequency assumes classes progress without overlaps. Overlaps or out-of-order intervals distort the running totals, making the identified median class unreliable and the interpolated median incorrect.
cfprev is the cumulative frequency just before the median class begins. It tells how many observations fall below the median class and anchors the interpolation inside that class.
If the median class has zero frequency, there is no density to interpolate within the class, so the formula divides by zero. Re-check the table or adjust class definitions.
CSV supports auditing and reruns in notebooks or pipelines, while PDF provides a consistent, shareable summary for reports. Together they preserve inputs, settings, and computed cumulative steps.
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.