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Median - Monomath Math Dictionary
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Median

Statistics

📖 Definition

The median is the middle value in a sorted dataset, dividing it into two equal halves.

📝 Detailed Explanation

To find the median, sort all values and select the middle number. For an odd count, it is the middle value. For an even count, it is the average of the two middle values. The median is robust to outliers (unlike the mean) and better represents typical values in skewed distributions, such as income or housing prices.

📐 Formula

If sorted: x_{(n+1)/2} for n odd; average of x_{n/2} and x_{n/2+1} for n even

📜 History & Origins

The median was used in earlier statistical studies but was formally named and developed in the 19th century. Francis Galton used medians in his studies of heredity. The median became widely used in the 20th century for economic and social statistics.

🔗 Related Terms

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