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The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic , being more resilient to outliers in a data set than the standard deviation . In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it.
More generally, a median is defined as a minimum of (| | | |), as discussed at Multivariate median (and specifically at Spatial median). This optimization-based definition of the median is useful in statistical data-analysis, for example, in k -medians clustering .
The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean. The median of a Cauchy distribution with location parameter x 0 and scale parameter y is x 0, the location parameter.
For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters.
The median absolute deviation (also MAD) is the median of the absolute deviation from the median. It is a robust estimator of dispersion . For the example {2, 2, 3, 4, 14}: 3 is the median, so the absolute deviations from the median are {1, 1, 0, 1, 11} (reordered as {0, 1, 1, 1, 11}) with a median of 1, in this case unaffected by the value of ...
People often think the MAPE will be optimized at the median. But for example, a log normal has a median of e μ {\displaystyle e^{\mu }} where as its MAPE is optimized at e μ − σ 2 {\displaystyle e^{\mu -\sigma ^{2}}} .
Absolute deviation in statistics is a metric that measures the overall difference between individual data points and a central value, typically the mean or median of a dataset. It is determined by taking the absolute value of the difference between each data point and the central value and then averaging these absolute differences. [4]
This interval is called the confidence interval, and the radius (half the interval) is called the margin of error, corresponding to a 95% confidence level. Generally, at a confidence level γ {\displaystyle \gamma } , a sample sized n {\displaystyle n} of a population having expected standard deviation σ {\displaystyle \sigma } has a margin of ...