Five number summaries, fractiles

There is Tukey's five number summary (minimum, lower hinge, median, upper hinge, maximum)

`fivenum(urb)`
and
`summary(urb)`
(same information as fivenum but with labels for the five values): in addition it also accepts matrices and data frames as arguments, e.g. summary(world) displays the five numbers for all numerical variables in world

In package LearnEDA there is an lval function:

`lval(urb)`

displaying all letter values for a variable.

Besides these functions, there are of course many functions meant to produce order statistics.

• median(urb) the median
• IRQ(urb) the interquartile range)
• range(urb) the range
• quantile(urb) function to produce any quantile (fractile); produces quantiles for a probability of 0,0.25, 0.5, 0.75 et 1). If you wish to produce other specific quantiles use the probs argument.
• quantile(urb,probs=0.10)
• quantile(urb,probs=c(0.33,0.66,1))
• boxplot.stats(urb) this ancillary function for boxplots can be used as such to produce the key values needed to display a boxplot. boxplot.stats(urb)\$stats returns five values: the end point of the lower whisker (the lower adjacent value), lower hinge, median, upper hinge and upper adjacent value. See help(boxplot.stats) for more details namely the returned values and options.

Remember that you always can use apply() to compute a statistic for a series of variables.

`apply(world,2,median)`

Computes the median for all variables (columns of world).