Median Calculator Form
Choose raw data, discrete frequency, or grouped frequency mode.
Example Data Table
| Example Type | Input | Median | Explanation |
|---|---|---|---|
| Raw Data | 3, 5, 7, 9, 11 | 7 | The middle value after sorting is 7. |
| Discrete Frequency | x: 2, 4, 6, 8 | f: 1, 2, 3, 2 | 6 | Cumulative frequency reaches the middle position at 6. |
| Grouped Frequency | 10-20, 20-30, 30-40 | f: 4, 7, 5 | 27.14 | The grouped median formula estimates the central value. |
Formula Used
1) Raw Data Median
Sort the values first.
Odd count: Median = x((n + 1) / 2)
Even count: Median = [x(n / 2) + x(n / 2 + 1)] / 2
2) Discrete Frequency Median
Use cumulative frequencies to find the middle observation position. If total frequency is even, average the two middle positions.
3) Grouped Frequency Median
Median = L + [((N / 2) - c.f.) / f] × h
L is the median class lower limit. N is total frequency. c.f. is cumulative frequency before the median class. f is median class frequency. h is class width.
How to Use This Calculator
- Select the correct calculation mode.
- Enter raw values, discrete values with frequencies, or grouped classes.
- Choose the number of decimal places.
- Add an optional report label.
- Click Calculate Median.
- Review the result, formula, table, and Plotly graph.
- Use the CSV or PDF buttons to export the analysis.
Median Algorithm Overview
- Read the dataset.
- Sort values or build cumulative frequencies.
- Find the total number of observations.
- Locate the middle observation position.
- Return the middle value or average two middle values.
- For grouped data, estimate the median using the median class formula.
Frequently Asked Questions
1) What does the median represent?
The median is the central value of an ordered dataset. Half the observations fall below it, and half fall above it.
2) When should I use median instead of mean?
Use the median when data contains outliers or strong skewness. It stays more stable than the mean in those situations.
3) Why must raw data be sorted first?
Sorting places observations in order. The median depends on middle positions, so the center cannot be identified correctly without sorting.
4) How does the calculator handle even counts?
It finds the two middle observations after ordering the data. Then it averages those two values to produce the median.
5) What are cumulative frequencies used for?
Cumulative frequencies help locate the middle observation position in frequency tables. They show how many observations have been counted up to each value or class.
6) Is grouped data median exact?
Grouped data median is an estimate. The exact individual observations are unknown, so the formula interpolates within the median class.
7) Can I export the results?
Yes. After calculation, you can download a CSV file and create a PDF report from the visible result section.
8) What input separators are supported?
You can separate values with commas, spaces, semicolons, or line breaks. Class intervals should use a lower-upper format like 10-20.