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Math and Simple Statistics in Rweb (Stat 3011)

Contents

Arithmetic

Some of the R language arithmetic operators are
R Operator Math Operation
+ addition
- subtraction
* multiplication
/ division
^ exponentiation
These operations operate elementwise on vectors. For example, see what these commands do 

     x <- c(1, 2, 3, 4)
     x + 2
     x^2

Math

Some R functions operate elementwise on vectors.
R Function Math Function
exp(x) ex
log(x) (natural) log of x
log10(x) common (base 10) log of x sqrt(x) square root

Other R functions operate on a vector and produce a single number (scalar).
R Function Math Function
sum(x) sum of elements of x
prod(x) product of elements of x
Thus the R idiom for calculating the sum of squares of the elements of a vector x is 

     sum(x^2)

R has a few predefined constants.
R Expression Math Constant Definition
pi 3.14159265... ratio of circumference and diameter of a circle
exp(1) 2.71828182... base of natural logarithms

Statistics

R has several functions operate on a vector considered as a data set and produce a summary statistic
R Function Statistics Function
mean(x) mean of the data set x
mean(x, trim = .10) 10% trimmed mean of the data set x
median(x) median of the data set x
var(x) sample variance of the data set x (divides by n - 1)
sd(x) sample standard deviation of the data set x, same as sqrt(var(x))
cor(x, y) correlation of the data sets x and y (which must be the same length).
IQR(x) interquartile range of the data set x,