In
descriptive statistics
A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and an ...
, a decile is any of the nine values that divide the sorted data into ten equal parts, so that each part represents 1/10 of the sample or population. A decile is one possible form of a
quantile
In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile th ...
; others include the
quartile and
percentile
In statistics, a ''k''-th percentile (percentile score or centile) is a score ''below which'' a given percentage ''k'' of scores in its frequency distribution falls (exclusive definition) or a score ''at or below which'' a given percentage fal ...
.
[.] A decile rank arranges the data in order from lowest to highest and is done on a scale of one to ten where each successive number corresponds to an increase of 10 percentage points.
Special Usage: The decile mean
A moderately robust measure of
central tendency
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.Weisberg H.F (1992) ''Central Tendency and Variability'', Sage University Paper Series on Quantitative Applications in ...
- known as the decile mean - can be computed by making use of a sample's deciles
to
(
= 10th percentile,
= 20th percentile and so on). It is calculated as follows:
:
Apart from serving as an alternative for the
mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the '' ari ...
and the
truncated mean
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low en ...
, it also forms the basis for robust measures of
skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined.
For a unimodal ...
and
kurtosis
In probability theory and statistics, kurtosis (from el, κυρτός, ''kyrtos'' or ''kurtos'', meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable. Like skewness, kurt ...
, and even a
normality test In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
More precisely, the tests are a fo ...
.
See also
*
Summary statistic
In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in
* a measure of ...
s
*
Socio-economic decile
In the New Zealand education system, decile is a key measure of socioeconomic status used to target funding and support schools. In academic contexts the full term "socioeconomic decile" or "socioeconomic decile band" may be used.
A school's dec ...
(for New Zealand schools)
References
Summary statistics
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de:Quantil#Dezil
ru:Квантиль#Дециль