Definition
The median is the middle value in a dataset when all values are arranged in order from smallest to largest. Exactly half of the values fall below the median and half fall above it. Unlike the mean, the median is not affected by extreme values, making it a robust measure of central tendency.
How to Find the Median
Sort your data from low to high. If there is an odd number of values, the median is the one right in the middle. If there is an even number, take the average of the two middle values.
Home prices on a street (in thousands): $150, $180, $200, $210, $950
Sorted from low to high, the middle value is the 3rd one: $200,000.
The mean would be $338,000 - pulled up by the $950,000 home. The median of $200,000 better represents the typical price.
Why It Matters
The median is the preferred measure of center whenever data is skewed or contains outliers. This is why government agencies report "median household income" rather than "mean household income" - a few extremely wealthy households would distort the average. The median gives a more honest picture of what is typical.
The median is also the foundation of box plots and percentile-based analyses. The 50th percentile is, by definition, the median.
Use the median when your data is skewed or has outliers. It tells you what the typical value actually is, without being distorted by extremes.