Median - The Middle Value of a Dataset
The median is the middle value of a dataset when all the values are arranged in order. It is a type of average that is not affected by very large or very small values (outliers), making it a reliable measure when data is skewed.
The word “median” comes from the Latin medianus, meaning “of the middle” – the exact same root that gives English the “median strip” running down the middle of a motorway. Government statisticians lean heavily on the median rather than the mean whenever reporting figures like income or house prices, precisely because a small number of billionaires or mansion sales can drag a mean far above what a typical household actually experiences; national median income is widely considered a fairer snapshot of how a typical family is really doing than the mean would give. This is exactly the same reason median house prices, rather than mean house prices, are almost always the figure quoted in property market news reports.
How to Find the Median
Step 1: Arrange all values in ascending order (smallest to largest).
Step 2: If there is an odd number of values, the median is the middle value.
Step 3: If there is an even number of values, the median is the mean of the two middle values.
Position of median = (n + 1) / 2, where n is the number of values.
Worked Examples
Ordered: 1, 3, 5, 7, 9. n = 5 (odd). Middle = 3rd value = 5.
Ordered: 4, 6, 8, 12, 16, 20. n = 6 (even). Two middle values = 8 and 12. Median = (8 + 12) / 2 = 10.
Ordered: 180,000 195,000 200,000 210,000 1,500,000.
Median = 200,000. Mean = 2,285,000 / 5 = 457,000.
The outlier (mansion) pulls the mean far above a typical price. The median better represents the street.
When to Use the Median
Use the median when the dataset contains outliers or is skewed. For example, median house prices, median salaries, or median age are often more informative than the mean in real-life reporting.
Key Takeaways
- Always sort the data before finding the median.
- Odd count: median = middle value. Even count: median = mean of two middle values.
- The median is not affected by outliers – it reflects the typical central value.
- Position formula: (n + 1) / 2 gives the position, not the value itself.