November 28th, 2016

Let’s look for a minute the data about US states

head(state.x77)

Population Income Illiteracy Life Exp Murder HS Grad Frost Area Alabama 3615 3624 2.1 69.05 15.1 41.3 20 50708 Alaska 365 6315 1.5 69.31 11.3 66.7 152 566432 Arizona 2212 4530 1.8 70.55 7.8 58.1 15 113417 Arkansas 2110 3378 1.9 70.66 10.1 39.9 65 51945 California 21198 5114 1.1 71.71 10.3 62.6 20 156361 Colorado 2541 4884 0.7 72.06 6.8 63.9 166 103766

What is the average of each column?

If we try directly with `mean()`

we get

mean(state.x77)

[1] 9956.887

That is the average of *everything*, which probably is not what we want

Instead we can use

colMeans(state.x77)

Population Income Illiteracy Life Exp Murder HS Grad Frost Area 4246.4200 4435.8000 1.1700 70.8786 7.3780 53.1080 104.4600 70735.8800

The result of `colMeans()`

is a *vector*. It can be plotted easily

barplot(colMeans(state.x77))

If all the columns are numeric, then we can also use `colMeans()`

in data frames

There are also other similar functions

`rowMeans()`

`colSums()`

`rowSums()`

For other cases we can use `apply()`

, which is more advanced

`apply()`

Please go to

Each question has 0 to 6 points. That way is easy to represent \[
0, \quad \frac{1}{6}, \quad \frac{1}{3},\quad\frac{1}{2},\quad\frac{2}{3},\quad \frac{5}{6},\quad 1
\] You can load them on R using `read.table()`