Median
Topic of Descriptive statistics, part of Data analysis
Median
| Type | Topic |
| Taught in | Descriptive statistics |
| Part | Data analysis |
| Questions using it | 4 |
The middle value of the ordered sample, or the average of the two middle values when n is even: the 0.5 sample quantile. Unlike the mean it barely moves when one value is wild, which makes it the robust summary of location. For a distribution it is any point m with \mathbb{P}(X\le m)\ge\tfrac12 and \mathbb{P}(X\ge m)\ge\tfrac12.
In Descriptive statistics
For data x_1,\ldots,x_n, the sample mean \overline x=\frac1n\sum x_i is the average and the sample median is the middle value of the sorted data, or the average of the two middle values when n is even. The median is robust: a single wild value can move the mean anywhere but barely moves the median.
Used in
- Taught in Descriptive statistics
- Also used in Statistical inference · Estimation · Regression examples · Linear model examples · Bayesian foundations · K-means clustering · Mixtures and the EM algorithm
- Questions that use it (4) — Distance to the nearest point · Summaries of ten cartons · An exponential rate · One thousand posterior draws
- All 2 questions on Descriptive statistics
See also
Sample quantile · Credible-region constructions · Five-number summary and boxplot · Posterior median · Posterior summaries from draws · R’s distribution interface · Interquartile range · Sample variance and standard deviation