Median

The median is the middle value of an ordered dataset or a 50th-percentile value of a probability distribution. It divides the observations or probability mass into halves, subject to conventions for ties and discrete distributions.

Order statistic: A value selected by its rank in an ordered sample. The sample median is the central order statistic, or an average of two central order statistics.
Middle value: The central item in a finite ordered list with an odd number of items. For an odd-sized sample, this item is the median.
Robust statistics: Statistical methods designed to remain informative when data contain outliers or model deviations. The median remains stable under extreme changes to a small number of observations.
Arithmetic mean: The sum of numerical values divided by their count. Unlike the median, the mean shifts substantially when extreme values are added.
Quantile: A value marking a specified proportion of observations or probability in a distribution. The median is the 0.5 quantile under common conventions.
Interpolation (statistics): A method for estimating a value between known data points. Some sample-quantile conventions interpolate between the two central observations.
Median absolute deviation: A robust measure of spread based on the median of absolute deviations from a center. It pairs the median with a scale estimate that is also resistant to outliers.
Mode (statistics): The most frequently occurring value in a dataset or the most probable value of a distribution. A mode identifies a peak, whereas the median identifies a halfway point.
Cumulative distribution function: A function giving the probability that a random variable is at most a specified value. The distribution median is located where cumulative probability reaches or straddles one half.
Weighted median: A value for which observations on either side each carry no more than half the total weight. Weights alter which point divides the sample's total influence into two halves.

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