R aggregate

aggregate() function splits a dataset into subsets, and executes summary statistics for each, then combine the results into a form to return.
aggregate(x, by, FUN, ..., simplify=TRUE, drop=TRUE) //for data frame
aggregate(formula, data, FUN, ..., subset, na.action=na.omit) //for formula
aggregate(x, nfrequency=1, FUN=sum, ndeltat=1, ts.eps=getOption("ts.eps"), ...) for time-series objects

by: a list of grouping elements, each as long as the variables in the data frame x. The elements are coerced to factors before use.
FUN: a function to compute the summary statistics which can be applied to all data subsets.
simplify: a logical indicating whether results should be simplified to a vector or matrix if possible.
formula: a formula, such as y ~ x or cbind(y1, y2) ~ x1 + x2, where the y variables are numeric data to be split into groups according to the grouping x variables (usually factors).
data: a data frame (or list) from which the variables in formula should be taken.
subset: an optional vector specifying a subset of observations to be used.
na.action: a function which indicates what should happen when the data contain NA values. The default is to ignore missing values in the given variables.
nfrequency: new number of observations per unit of time; must be a divisor of the frequency of x.
ndeltat: new fraction of the sampling period between successive observations; must be a divisor of the sampling interval of x.
ts.eps: tolerance used to decide if nfrequency is a sub-multiple of the original frequency.

Let's use the builtin dataset CO2 (Carbon Dioxide Uptake in Grass Plants).
> CO2

Plant Type Treatment conc uptake 1 Qn1 Quebec nonchilled 95 16.0 2 Qn1 Quebec nonchilled 175 30.4 3 Qn1 Quebec nonchilled 250 34.8 4 Qn1 Quebec nonchilled 350 37.2 5 Qn1 Quebec nonchilled 500 35.3 6 Qn1 Quebec nonchilled 675 39.2 7 Qn1 Quebec nonchilled 1000 39.7 8 Qn2 Quebec nonchilled 95 13.6 9 Qn2 Quebec nonchilled 175 27.3 10 Qn2 Quebec nonchilled 250 37.1 11 Qn2 Quebec nonchilled 350 41.8 12 Qn2 Quebec nonchilled 500 40.6 13 Qn2 Quebec nonchilled 675 41.4 14 Qn2 Quebec nonchilled 1000 44.3 15 Qn3 Quebec nonchilled 95 16.2 16 Qn3 Quebec nonchilled 175 32.4 17 Qn3 Quebec nonchilled 250 40.3 18 Qn3 Quebec nonchilled 350 42.1 19 Qn3 Quebec nonchilled 500 42.9 20 Qn3 Quebec nonchilled 675 43.9 21 Qn3 Quebec nonchilled 1000 45.5 22 Qc1 Quebec chilled 95 14.2 23 Qc1 Quebec chilled 175 24.1 24 Qc1 Quebec chilled 250 30.3 25 Qc1 Quebec chilled 350 34.6 26 Qc1 Quebec chilled 500 32.5 27 Qc1 Quebec chilled 675 35.4 28 Qc1 Quebec chilled 1000 38.7 29 Qc2 Quebec chilled 95 9.3 30 Qc2 Quebec chilled 175 27.3 31 Qc2 Quebec chilled 250 35.0 32 Qc2 Quebec chilled 350 38.8 33 Qc2 Quebec chilled 500 38.6 34 Qc2 Quebec chilled 675 37.5 35 Qc2 Quebec chilled 1000 42.4 36 Qc3 Quebec chilled 95 15.1 37 Qc3 Quebec chilled 175 21.0 38 Qc3 Quebec chilled 250 38.1 39 Qc3 Quebec chilled 350 34.0 40 Qc3 Quebec chilled 500 38.9 41 Qc3 Quebec chilled 675 39.6 42 Qc3 Quebec chilled 1000 41.4 43 Mn1 Mississippi nonchilled 95 10.6 44 Mn1 Mississippi nonchilled 175 19.2 45 Mn1 Mississippi nonchilled 250 26.2 46 Mn1 Mississippi nonchilled 350 30.0 47 Mn1 Mississippi nonchilled 500 30.9 48 Mn1 Mississippi nonchilled 675 32.4 49 Mn1 Mississippi nonchilled 1000 35.5 50 Mn2 Mississippi nonchilled 95 12.0 51 Mn2 Mississippi nonchilled 175 22.0 52 Mn2 Mississippi nonchilled 250 30.6 53 Mn2 Mississippi nonchilled 350 31.8 54 Mn2 Mississippi nonchilled 500 32.4 55 Mn2 Mississippi nonchilled 675 31.1 56 Mn2 Mississippi nonchilled 1000 31.5 57 Mn3 Mississippi nonchilled 95 11.3 58 Mn3 Mississippi nonchilled 175 19.4 59 Mn3 Mississippi nonchilled 250 25.8 60 Mn3 Mississippi nonchilled 350 27.9 61 Mn3 Mississippi nonchilled 500 28.5 62 Mn3 Mississippi nonchilled 675 28.1 63 Mn3 Mississippi nonchilled 1000 27.8 64 Mc1 Mississippi chilled 95 10.5 65 Mc1 Mississippi chilled 175 14.9 66 Mc1 Mississippi chilled 250 18.1 67 Mc1 Mississippi chilled 350 18.9 68 Mc1 Mississippi chilled 500 19.5 69 Mc1 Mississippi chilled 675 22.2 70 Mc1 Mississippi chilled 1000 21.9 71 Mc2 Mississippi chilled 95 7.7 72 Mc2 Mississippi chilled 175 11.4 73 Mc2 Mississippi chilled 250 12.3 74 Mc2 Mississippi chilled 350 13.0 75 Mc2 Mississippi chilled 500 12.5 76 Mc2 Mississippi chilled 675 13.7 77 Mc2 Mississippi chilled 1000 14.4 78 Mc3 Mississippi chilled 95 10.6 79 Mc3 Mississippi chilled 175 18.0 80 Mc3 Mississippi chilled 250 17.9 81 Mc3 Mississippi chilled 350 17.9 82 Mc3 Mississippi chilled 500 17.9 83 Mc3 Mississippi chilled 675 18.9 84 Mc3 Mississippi chilled 1000 19.9

> aggregate(CO2$uptake,by=list(Plant=CO2$Plant),FUN=mean)
   Plant        x
1    Qn1 33.22857
2    Qn2 35.15714
3    Qn3 37.61429
4    Qc1 29.97143
5    Qc3 32.58571
6    Qc2 32.70000
7    Mn3 24.11429
8    Mn2 27.34286
9    Mn1 26.40000
10   Mc2 12.14286
11   Mc3 17.30000
12   Mc1 18.00000

> aggregate(formula=uptake ~ conc, data=CO2, FUN=mean)
  conc   uptake
1   95 12.25833
2  175 22.28333
3  250 28.87500
4  350 30.66667
5  500 30.87500
6  675 31.95000
7 1000 33.58333

> aggregate(formula=cbind(uptake,conc) ~ Plant, data=CO2, FUN=mean)
   Plant   uptake conc
1    Qn1 33.22857  435
2    Qn2 35.15714  435
3    Qn3 37.61429  435
4    Qc1 29.97143  435
5    Qc3 32.58571  435
6    Qc2 32.70000  435
7    Mn3 24.11429  435
8    Mn2 27.34286  435
9    Mn1 26.40000  435
10   Mc2 12.14286  435
11   Mc3 17.30000  435
12   Mc1 18.00000  435