statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, the quartile coefficient of dispersion () is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the

coefficient of variation In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability ...

. As such, it is one of several robust measures of scale. The statistic is easily computed using the first and third

quartile In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or ''quarters'', of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are ...

s, and , respectively) for each data set. The quartile coefficient of dispersion is the ratio of half of 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 differen ...

() to the average of the quartiles (the

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. The midhinge is defined as \begin \operato ...

\begin
\mathrm &= \frac \\
&= .
\end

Example

Consider the following two data sets: : ''A'' = :: ''n'' = 7, range = 12, mean = 8, median = 8, ''Q''₁ = 4, ''Q''₃ = 12, quartile coefficient of dispersion = 0.5 : ''B'' = :: ''n'' = 7, range = 1.2, mean = 2.4, median = 2.4, ''Q''₁ = 2, ''Q''₃ = 2.9, quartile coefficient of dispersion = 0.18 The quartile coefficient of dispersion of data set ''A'' is 2.7 times as great (0.5 / 0.18) as that of data set ''B''.

References

Statistical deviation and dispersion Statistical ratios {{statistics-stub

Example

See also

References