|
For loudspeakers, see mid-range speakerIn statistics, the midrange of a set of statistical data values is the arithmetic mean of the smallest and largest values in the set. As such it is a measure of central tendency. It is highly sensitive to outliers and ignores all but two data points; therefore it is rarely used in statistical analysis. A limited amount of experimental work on the efficiency of measures of central tendency for small samples by William D. Vinson reveals the following facts values of γ2 Most efficient Estimator of μ -1.2 to -0.8 Mid Range -0.8 to 2.0 Arithmetic Mean 2.0 to 6.0 Modified Mean This generalization holds for sample sizes from 3 to 20, except when n = 3. When n=3 there can be no modified mean, and the mean is the most effiient measure of central tendencyfor values of γ2 form 2.0 to 6.0 as well as from -0.8 to 2.0. Where γ2 = (μ4/(μ2)²)-3 Further more, mid range is an inefficient estimator of μ when the population is normal.However, for a sufficiently platykurtic distribution the mid range is by far the most efficient estimator. While the mean of a set of values minimises the sum of squares of deviations and the median minimises the average absolute deviation, the midrange minimises the maximum deviation.
| ||||||||
|
| |||||||||
 |
|
| |