Mediana

Mediana is the term used in Spanish, Portuguese, Italian, and several other Romance languages for the statistical concept known in English as the median. In statistics, the median is a measure of central tendency that identifies the value separating the higher half from the lower half of a data set, probability distribution, or population. It is the 50th percentile, meaning that at least half of the observations are less than or equal to the median and at least half are greater than or equal to it【1†L1-L4】.

Definition and Calculation

• Discrete data sets:

  • If the number of observations n is odd, the median is the middle value after the data are ordered in ascending (or descending) order.
  • If n is even, the median is conventionally defined as the arithmetic mean of the two central values (the n/2‑th and (n/2 + 1)‑th observations).

• Continuous probability distributions:

  • The median m satisfies the equation F(m) = 0.5, where F is the cumulative distribution function (CDF). In other words, the probability that a random variable X is less than or equal to m is one half.

These definitions make the median a robust statistic, less sensitive to extreme values (outliers) than the arithmetic mean【1†L1-L4】.

Applications

The median is widely employed in fields such as economics (e.g., median household income), epidemiology (median survival time), environmental science (median pollutant concentrations), and any discipline where a representative central value is required without undue influence from outliers.

Historical and Etymological Notes

The English word median derives from the Latin adjective medianus (“situated in the middle”), which entered English via Old French mediane. The Romance‑language forms—mediana (Spanish, Portuguese), mediana (Italian), mediane (French)—share this Latin root.

Comparison with Related Measures

• Mean (average): The arithmetic mean sums all observations and divides by their count; it can be heavily affected by extreme values.
• Mode: The most frequently occurring value(s) in a data set; a data set may have multiple modes or none.

Because the median partitions the data into two equally sized halves, it provides a simple yet informative summary of distributional location, especially for skewed data where the mean may be misleading.

References

1. “Median.” Wikipedia, the free encyclopedia. https://en.wikipedia.org/wiki/Median (accessed 11 April 2026).