Find grouped median and median class clearly. Check cumulative frequencies, boundaries, width, and totals quickly. Build summaries for exams, research, quality checks, and reporting.
| Class Interval | Frequency |
|---|---|
| 0-10 | 5 |
| 10-20 | 9 |
| 20-30 | 12 |
| 30-40 | 7 |
| 40-50 | 3 |
Median = L + [((N / 2) - cf) / f] × h
Grouped data median helps summarize a frequency distribution when raw observations are unavailable. It identifies the central value from class intervals and frequencies. This makes it useful for exam scores, survey ranges, salary bands, production counts, and quality summaries. The measure is resistant to extreme values. That feature makes it stronger than the mean in skewed distributions. In applied statistics, the grouped median gives a reliable picture of the center without needing every original record.
The method first adds frequencies to build cumulative frequency. Then it finds N divided by 2. The class where cumulative frequency first reaches that value becomes the median class. After that, the formula uses the lower boundary, class width, previous cumulative frequency, and class frequency. This interpolation step estimates where the middle value falls inside the median class. The result is more precise than choosing only the class midpoint.
Students use grouped median calculators in school statistics, business math, economics, and research methods. Teachers use them for classroom summaries. Analysts use them for grouped customer age data, grouped income tables, time ranges, and defect counts. Researchers also use grouped median results when tables are published without raw data. Because the process is standardized, the output is easy to explain in reports, assignments, and audit notes.
This calculator shows the total frequency, N divided by 2, the median class, and each step used in the interpolation formula. The cumulative frequency table helps verify the chosen class quickly. The boundary adjustment option supports inclusive class intervals such as 10-19 and 20-29. CSV and PDF exports help save working notes. When you compare several grouped distributions, the median is a practical center measure that stays stable and interpretable.
The grouped data median is the estimated middle value of a grouped frequency distribution. It splits the total frequency into two equal parts using the median class and interpolation formula.
Cumulative frequency helps locate the median class. You compare each running total with N divided by 2. The first class that reaches or exceeds that value contains the grouped median.
Use 0.5 when your class intervals are inclusive integer groups, such as 10-19 and 20-29. That correction converts class limits into continuous boundaries for accurate median estimation.
Yes. You can enter decimal class intervals and decimal frequencies. The calculator sorts the classes, builds cumulative frequency, and returns the grouped median with your selected decimal precision.
No. The formula uses the width of the actual median class. Equal widths are common, but the grouped median can still be estimated when class widths differ.
No. Raw median uses original observations. Grouped median is an estimate based on class intervals and frequencies. It is very useful when only summarized frequency tables are available.
The median is less affected by extreme values. In skewed grouped data, it can describe the center more fairly than the mean, especially for income, cost, and time distributions.
Common causes include invalid interval order, wrong frequencies, incorrect boundary adjustment, or entering class labels in the wrong format. Always check the detailed table after calculation.
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.