Median Calculator
Find the median of any dataset in seconds. Get step-by-step solutions, interactive charts, and export your results to Word, PDF, or Excel.
📦 Box Plot & Distribution
📊 Frequency Histogram
How to Write Your Results
The median is the best measure of centre when data is skewed or contains outliers — such as income data, real estate prices, or ecological survey counts.
- Data is skewed left or right and the mean would be misleading
- Outliers are present and you do not want them to distort the average
- You need to find the exact middle value of a ranked dataset
- Reporting income, house prices, or survival times where extremes exist
- You are working with ordinal data (e.g. Likert scale responses)
💰 Finance & Economics
Median household income is more representative than mean income because a few ultra-wealthy earners skew the mean upward.
🏠 Real Estate
Median house prices report the typical property more accurately when a few luxury homes inflate the mean.
🏥 Healthcare
Median survival time in clinical trials is the preferred central tendency measure — more interpretable than the mean for skewed distributions.
🦁 Ecology & Wildlife
Species abundance counts often have extreme values (zero-inflation or rare spikes). The median captures the typical observation accurately.
Decision Tree: Mean vs Median vs Mode
Median Formula
Step 1: Sort the dataset in ascending order: x₁ ≤ x₂ ≤ … ≤ xₙ
Where: n = number of observations, x = sorted values
Grouped Frequency Table Median
Where: L = lower class boundary of the median class; n = total frequency; F = cumulative frequency before the median class; f = frequency of the median class; h = class width
Interquartile Range (IQR) & Quartiles
Values beyond the fences are flagged as potential outliers.
Relationship: Median, Mean & Skewness
Pearson's Second Coefficient of Skewness approximation:
Positive value = right-skewed (mean > median). Negative = left-skewed (mean < median). Near zero = symmetric.
Enter or paste your data
Type or paste numbers in the input box separated by commas or new lines. Example: 12, 7, 3, 14, 6.
Or choose a sample dataset
Select from five pre-built sample datasets (salaries, scores, heights, prices, ecology) using the dropdown menu to explore instantly.
Or upload a file
Click the Upload tab and drag in a .csv, .txt, .xlsx, or .xls file. A column picker will appear to select the numeric column you want to analyse.
Or use Manual Entry
Switch to the Manual tab, enter the number of values you want to input, and fill each field individually.
Click "Calculate Median"
Press the green button. The calculator will sort your data, find the middle position, and return the median instantly.
Review step-by-step workings
The sorted array is displayed with the median value(s) highlighted in green so you can follow exactly how the answer was computed.
Read the statistics table
A full summary table shows median, mean, mode, Q1, Q3, IQR, SD, variance, skewness, kurtosis, min, max, and range.
Interpret the charts
A box plot shows the five-number summary and outliers. A histogram shows the frequency distribution with the median marked as a vertical line.
Read the interpretation
The interpretation section explains what the median means in plain language and provides APA 7th, thesis, and plain-language write-up templates.
Export your results
Download a full 8-section report as a Word document, PDF, Excel spreadsheet, or plain text file using the export buttons.
| Assumption | Required? | Notes |
|---|---|---|
| Numeric data | Yes | All values must be numbers (integers or decimals) |
| Ordinal or continuous scale | Yes | Median is meaningful for ordinal and higher scales |
| Normality | No | The median is non-parametric — no normality required |
| Minimum sample size | Recommended n ≥ 3 | Works with any n ≥ 1; more data = more reliable estimate |
| Independent observations | Recommended | Not strictly required for descriptive use |
| No outliers | No | The median is robust to outliers — this is its key advantage |
What is the median in statistics?
How do you find the median of a data set?
What is the median formula?
When should I use the median instead of the mean?
What is the median for an even number of values?
Is the median the same as the 50th percentile?
Can the median be used with grouped data or frequency tables?
What is the difference between median and mean?
How does this median calculator work?
What are real-world examples of the median?
The following sources underpin the median calculator, median formula, and statistical principles covered on this page. Key concepts including the median of a data set, step-by-step calculation, and how to find the median in skewed distributions are grounded in established statistical literature.
- Agresti, A., & Franklin, C. (2021). Statistics: The Art and Science of Learning from Data (5th ed.). Pearson. https://www.pearson.com
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
- Hogg, R. V., McKean, J. W., & Craig, A. T. (2019). Introduction to Mathematical Statistics (8th ed.). Pearson.
- Navidi, W. (2022). Statistics for Engineers and Scientists (5th ed.). McGraw-Hill Education.
- Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics (9th ed.). W. H. Freeman.
- Walpole, R. E., Myers, R. H., & Myers, S. L. (2016). Probability and Statistics for Engineers and Scientists (9th ed.). Pearson.
- Casella, G., & Berger, R. L. (2002). Statistical Inference (2nd ed.). Duxbury Press.
- Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley.
- National Institute of Standards and Technology. (2023). NIST/SEMATECH e-Handbook of Statistical Methods. https://www.itl.nist.gov/div898/handbook/
- American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.). APA. https://doi.org/10.1037/0000165-000
- Pearson, K. (1895). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society, 186, 343–414. https://doi.org/10.1098/rsta.1895.0010
- Galton, F. (1881). Report of the anthropometric committee. Report of the British Association for the Advancement of Science, 245–260.
- Hyndman, R. J., & Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician, 50(4), 361–365. https://doi.org/10.2307/2684934