California had the most murders, but does this mean it is the most dangerous state? What if it just has many more people than any other state? We can quickly confirm that California indeed has the largest population:
library(dslabs)
data("murders")
murders$state[which.max(murders$population)]
#> [1] "California"
with over 37 million inhabitants. It is therefore unfair to compare the totals if we are interested in learning how safe the state is. What we really should be computing is the murders per capita. The reports we describe in the motivating section used murders per 100,000 as the unit. To compute this quantity, the powerful vector arithmetic capabilities of R come in handy.
In R, arithmetic operations on vectors occur element-wise. For a quick example, suppose we have height in inches:
inches <- c(69, 62, 66, 70, 70, 73, 67, 73, 67, 70)
and want to convert to centimeters. Notice what happens when we multiply
inches by 2.54:
inches * 2.54
#> [1] 175 157 168 178 178 185 170 185 170 178
In the line above, we multiplied each element by 2.54. Similarly, if for each entry we want to compute how many inches taller or shorter than 69 inches, the average height for males, we can subtract it from every entry like this:
inches - 69
#> [1] 0 -7 -3 1 1 4 -2 4 -2 1
If we have two vectors of the same length, and we sum them in R, they will be added entry by entry as follows:
\[\begin{pmatrix} a\\ b\\ c\\ d \end{pmatrix} + \begin{pmatrix} e\\ f\\ g\\ h \end{pmatrix} = \begin{pmatrix} a +e\\ b + f\\ c + g\\ d + h \end{pmatrix}\]The same holds for other mathematical operations, such as -, * and
/.
This implies that to compute the murder rates we can simply type:
murder_rate <- murders$total / murders$population * 100000
Once we do this, we notice that California is no longer near the top of the list. In fact, we can use what we have learned to order the states by murder rate:
murders$abb[order(murder_rate)]
#> [1] "VT" "NH" "HI" "ND" "IA" "ID" "UT" "ME" "WY" "OR" "SD" "MN" "MT"
#> [14] "CO" "WA" "WV" "RI" "WI" "NE" "MA" "IN" "KS" "NY" "KY" "AK" "OH"
#> [27] "CT" "NJ" "AL" "IL" "OK" "NC" "NV" "VA" "AR" "TX" "NM" "CA" "FL"
#> [40] "TN" "PA" "AZ" "GA" "MS" "MI" "DE" "SC" "MD" "MO" "LA" "DC"