Statistics · BEGINNER LESSON
Median
The median is the middle value in an ordered set of numbers; it is also the 50th percentile, meaning half the values are at or below it and half are at or above it. When there are two middle values, the median is their average.
What the median is
The median is a measure of central tendency, also called a measure of location, because it describes the middle of a data set. To find it, the values must first be arranged in order, usually from smallest to largest. In an ordered list, the median is the point with half the observations below it and half above it. This is why it is also called the 50th percentile.
[1] Median - StatPearls - NCBI Bookshelf [2] Measures of central tendency: Median and mode - PMC - NIH [3] 1.3.5.1. Measures of Location
How it is found
If the number of values is odd, the median is the middle item in the ordered list. If the number is even, there are two middle items, and the median is the average of those two numbers. For example, in a sorted list with seven values, the fourth value is the median. This method uses rank rather than the size of every gap between values.
[1] Median - StatPearls - NCBI Bookshelf [2] Measures of central tendency: Median and mode - PMC - NIH
Why it is useful
The median is less affected by outliers, which are unusually high or low values. In skewed data, extreme values can pull the mean, or arithmetic average, away from the center, while the median often stays closer to the typical middle. Because of this, the median can better represent location in data with extreme tails or uneven spread. It is also used with ordinal data, where values can be ordered but not measured with equal numerical spacing.
[1] Median - StatPearls - NCBI Bookshelf [2] Measures of central tendency: Median and mode - PMC - NIH [3] 1.3.5.1. Measures of Location
Limits of the median
The median does not use the exact value of every observation, so it leaves out some detail. It is also not always the best summary when data have multiple peaks, such as bimodal or multimodal distributions, because a single middle value may fall in a gap between clusters. In those cases, mean, mode, or other summaries may be more informative depending on the question.
[1] Median - StatPearls - NCBI Bookshelf [2] Measures of central tendency: Median and mode - PMC - NIH [3] 1.3.5.1. Measures of Location
SEE THE IDEA
How the median is obtained
Sort numbers from low to high so positions can be counted.
Use the center item if there is an odd count.
If there is an even count, average the two center items.
The median marks the halfway point of the ordered data.
Each step depends on the previous one: ordering makes the middle position visible, then the middle value is selected or averaged.
The median is a position-based summary of the middle of ordered data.
TRY IT YOURSELF
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.