Glossary
Median
The median is the middle value of an ordered dataset. If there is an even number of observations, it is the average of the two central values. As a measure of central tendency, the median is more robust to outliers than the arithmetic mean, making it the preferred choice for s...
Definition
The median is the middle value of an ordered dataset. If there is an even number of observations, it is the average of the two central values. As a measure of central tendency, the median is more robust to outliers than the arithmetic mean, making it the preferred choice for skewed distributions.
Why It Matters
Income, house prices, and response times are typically right-skewed, meaning a few extreme high values pull the mean upward. The median remains unaffected by these extremes and therefore gives a truer picture of the "typical" case. It is also the appropriate measure for ordinal data where the mean has no meaningful interpretation.
Example
A hospital reports that the median waiting time in A&E is 45 minutes, while the mean is 72 minutes. The difference arises because a small number of patients with complex emergencies wait several hours. For operational planning and patient communication, the median of 45 minutes is the more honest and useful figure.
Related Terms
Software Notes
- SPSS: Analyze > Descriptive Statistics > Frequencies or Explore. Select "Median" under Statistics.
- R:
median(x, na.rm = TRUE). For grouped data:aggregate(y ~ group, data = df, median). - Stata:
summarize varname, detailreports the median in the "p50" row.centile varnamecomputes confidence intervals for the median.