What is Median?
The median is a measure of central tendency that represents the middle value in a sorted dataset.
Unlike the arithmetic mean (average), the median is not affected by extreme values or outliers. This makes it a more robust measure of central tendency when your data contains unusually high or low values that could skew the average.
The median is widely used in statistics, economics, and data analysis. Common applications include reporting median household income (which better represents typical earnings than the mean), real estate prices, and any dataset where outliers could distort the average.
Median Formula
To calculate the median manually, follow these steps:
The median is the middle value in a sorted dataset. If there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.
Example Calculation
For the dataset [3, 7, 9, 12, 15], the median is 9 (the middle value). For [3, 7, 9, 12, 15, 18], the median is (9 + 12) / 2 = 10.5 (average of the two middle values).
When to Use Median
The median is the preferred measure of central tendency in many real-world scenarios:
Income Statistics
Median household income is more representative than mean income because a few extremely wealthy individuals can dramatically inflate the average, while the median shows what a typical household earns.
Real Estate Prices
Median home prices are often reported instead of averages because luxury properties can skew the mean upward, making the median a better indicator of typical market prices.
Test Scores Analysis
When analyzing test scores with potential outliers (students who scored exceptionally high or low), the median provides a better sense of how most students performed.