iqr | R Documentation |
Compute the interquartile range for a set of data.
iqr(x, na.rm = FALSE)
x |
numeric vector of observations. |
na.rm |
logical scalar indicating whether to remove missing values from |
Let \underline{x}
denote a random sample of n
observations from
some distribution associated with a random variable X
. The sample
interquartile range is defined as:
IQR = \hat{X}_{0.75} - \hat{X}_{0.25} \;\;\;\;\;\; (1)
where X_p
denotes the p
'th quantile of the distribution and
\hat{X}_p
denotes the estimate of this quantile (i.e., the sample
p
'th quantile).
See the R help file for quantile
for information on how sample
quantiles are computed.
A numeric scalar – the interquartile range.
The interquartile range is a robust estimate of the spread of the
distribution. It is the distance between the two ends of a boxplot
(see the R help file for boxplot
). For a normal distribution
with standard deviation \sigma
it can be shown that:
IQR = 1.34898 \sigma \;\;\;\;\;\; (2)
Steven P. Millard (EnvStats@ProbStatInfo.com)
Chambers, J.M., W.S. Cleveland, B. Kleiner, and P.A. Tukey. (1983). Graphical Methods for Data Analysis. Duxbury Press, Boston, MA.
Cleveland, W.S. (1993). Visualizing Data. Hobart Press, Summit, New Jersey.
Helsel, D.R., and R.M. Hirsch. (1992). Statistical Methods in Water Resources Research. Elsevier, New York, NY.
Hirsch, R.M., D.R. Helsel, T.A. Cohn, and E.J. Gilroy. (1993). Statistical Analysis of Hydrologic Data. In: Maidment, D.R., ed. Handbook of Hydrology. McGraw-Hill, New York, Chapter 17, pp.5–7.
Zar, J.H. (2010). Biostatistical Analysis. Fifth Edition. Prentice-Hall, Upper Saddle River, NJ.
Summary Statistics, summaryFull
,
var
, sd
.
# Generate 20 observations from a normal distribution with parameters
# mean=10 and sd=2, and compute the standard deviation and
# interquartile range.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(250)
dat <- rnorm(20, mean=10, sd=2)
sd(dat)
#[1] 1.180226
iqr(dat)
#[1] 1.489932
#----------
# Repeat the last example, but add a couple of large "outliers" to the
# data. Note that the estimated standard deviation is greatly affected
# by the outliers, while the interquartile range is not.
summaryStats(dat, quartiles = TRUE)
# N Mean SD Median Min Max 1st Qu. 3rd Qu.
#dat 20 9.8612 1.1802 9.6978 7.6042 11.8756 9.1618 10.6517
new.dat <- c(dat, 20, 50)
sd(dat)
#[1] 1.180226
sd(new.dat)
#[1] 8.79796
iqr(dat)
#[1] 1.489932
iqr(new.dat)
#[1] 1.851472
#----------
# Clean up
rm(dat, new.dat)
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