In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, the interdecile range is the difference between the first and the ninth
deciles (10% and 90%). The interdecile range is a measure of
statistical dispersion of the values in a set of data, similar to the
range
Range may refer to:
Geography
* Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra)
** Mountain range, a group of mountains bordered by lowlands
* Range, a term used to i ...
and the
interquartile range
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference ...
, and can be computed from the (non-parametric)
seven-number summary.
Despite its simplicity, the interdecile range of a sample drawn from a normal distribution can be divided by 2.56 to give a reasonably
efficient estimator of the standard deviation of a normal distribution. This is derived from the fact that the lower (respectively upper) decile of a normal distribution with arbitrary
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...
is equal to the mean minus (respectively, plus) 1.28 times the standard deviation.
A more efficient estimator is given by instead taking the 7% trimmed range (the difference between the 7th and 93rd percentiles) and dividing by 3 (corresponding to 86% of the data falling within ±1.5 standard deviations of the mean in a normal distribution); this yields an estimator having about 65% efficiency. Analogous measures of location are given by the
median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic fe ...
,
midhinge In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location.
Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator.
: \operatorname(X) = \overline = \frac = \frac = M ...
, and
trimean In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles:
: TM= \frac
This is equivalent to the average of the med ...
(or statistics based on nearby points).
See also
*
Interquartile range
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference ...
*
Robust measures of scale In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the ''interquartile range'' (IQR) and the ''median absol ...
*
Standard deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while ...
*
Statistical analysis
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability.Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. . Inferential statistical analysis infers propertie ...
References
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{{DEFAULTSORT:Interdecile Range
Scale statistics