Formula & Calculator
Median
Finds the middle value of a sorted dataset, a measure of central tendency that is robust to outliers.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Median | Median value | |
| n | Number of data points |
What it means
The median is the value that separates the lower half of a sorted dataset from the upper half. It is a measure of central tendency that is robust to extreme values, unlike the mean. For an odd number of observations, it is the middle value; for an even number, it is the average of the two middle values. The median is commonly used in reporting income, house prices, and other distributions that are often skewed. It is also used in non‑parametric statistics. Understanding the median is important for interpreting data where outliers could distort the average. It provides a more "typical" value in skewed distributions.
Worked example
Median – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Sorted Data | 1,3,5,7,9 |
| n | 5 |
| Parameter | Value |
|---|---|
| Sorted Data | 2,4,6,8 |
| n | 4 |
Common mistakes
- Sorting: Always sort the data in ascending order before finding the median.
- Even n: If the number of values is even, take the average of the two middle numbers.
- Odd n: The median is the exact middle value.
- Robustness: The median is robust to outliers, unlike the mean.
- Data type: Applicable to ordinal and continuous data – not nominal.
Applications
The median is the middle value of a sorted dataset, separating the higher half from the lower half. It is a robust measure of central tendency, less affected by outliers than the mean. Engineers use it when data are skewed, such as in material strength tests or reliability data. In economics, median income better represents typical earnings than the mean. In healthcare, it describes patient waiting times. By using the median, professionals can provide a more accurate summary of non‑normal distributions. It is also used in descriptive statistics and in constructing box plots. Understanding the median is crucial for interpreting data with extreme values, ensuring that conclusions are not distorted by a few unusual observations.
- Income and salary reporting (less influenced by extremes)
- Reliability and lifetime data analysis (skewed distributions)
- Healthcare – patient waiting times and treatment durations
- Real estate – property price summaries
- Quality control – when data are not normally distributed