In
statistics, the quartile coefficient of dispersion is a descriptive statistic which measures
dispersion
Dispersion may refer to:
Economics and finance
* Dispersion (finance), a measure for the statistical distribution of portfolio returns
* Price dispersion, a variation in prices across sellers of the same item
*Wage dispersion, the amount of variat ...
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. As such, it is one of several
robust measures of scale.
The statistic is easily computed using the first (''Q''
1) and third (''Q''
3)
quartiles for each data set. The quartile coefficient of dispersion is:
:
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''.
See also
*
Robust measures of scale
*
Coefficient of variation
*
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 ...
*
Median absolute deviation
In statistics, the median absolute deviation (MAD) is a robust measure of the variability of a univariate sample of quantitative data. It can also refer to the population parameter that is estimated by the MAD calculated from a sample.
For a u ...
References
Statistical deviation and dispersion
Statistical ratios
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