1

Write a function with the name standardize that normalizes the values of a given vector with the following formula:

\[(x - \bar{x}) / S\]

where \(x\) is each input value, \(\bar{x}\) is the sample mean value and \(S\) the sample standard deviation.

The base R function for computing the standard deviation function is sd(). Don’t forget to use the option na.rm = TRUE and be careful when setting the brackets around the formula.

solution 

standardize <- function (x) {
  (x - mean(x, na.rm = TRUE)) / sd(x, na.rm = TRUE)
}

As a preparation for the next task, please run the following code create a vector with 30 randomly selected values.

vector <- sample(1:100, 30)

2

Feed the vector into your standardize() function to see if it works.

solution 

standardize(vector)
##  [1] -0.44409780 -0.56822451 -0.65097566  1.74880749 -1.35436037 -0.98198023 -0.11309323 -1.18885809 -1.14748252 -0.85785351
## [11] -0.94060466  1.33505177  1.04542277  0.46616477  0.30066249 -1.27160923 -0.19584437  0.38341363  0.92129606  0.13516020
## [21]  1.62468077  0.71441820 -0.89922909 -1.02335580  0.83854491  1.37642734  1.91430977 -0.69235123  0.01103349 -0.48547337

3

Write an if-else statement that checks whether the first element of the standardized vector is smaller than 0. If this condition is true, “TRUE” should be printed. If this condition is false, “FALSE” should be printed.

Make use of logical operators (<) to check if a condition is true or false. For printing, you should use the print() function.

solution 

if (standardize(vector)[1] < 0) {
  print("TRUE")
} else {
  print("FALSE")
}
## [1] "TRUE"