Class activity, September 4 solutions

Writing a function to calculate the mean

The mean of numbers \(x_1,...,x_n\) is their average:

\[\frac{x_1 + x_2 + \cdots + x_n}{n}\] In R, we can calculate the mean with the mean function. For example:

mean(c(1,2,3))

[1] 2

1. Write your own mean function, called my_mean, that calculates the mean of a vector. The input to your function should be a vector, and the output should be the mean of the values in that vector. You may not use the built-in mean function in R, but you may use the sum and length functions.

my_mean <- function(x){
  return(sum(x)/length(x))
}

2. Check that your function works by comparing the output with R’s mean function for several different input vectors.

my_mean(1:10)

[1] 5.5

mean(1:10)

[1] 5.5

unif_samp <- runif(100)
my_mean(unif_samp)

[1] 0.4952387

mean(unif_samp)

[1] 0.4952387

Weighted means

A weighted mean is similar to the usual average, but now we add a weight to each value. The observations with greater weights contribute more to the weighted mean.

The weighted mean of \(x_1,...,x_n\) with weights \(w_1,...,w_n\) is

\[\frac{w_1 x_1 + w_2 x_2 + \cdots + w_n x_n}{w_1 + w_2 + \cdots + w_n}\] The usual arithmetic mean is a special case of the weighted mean with \(w_1 = w_2 = \cdots = w_n = 1\).

3. Modify your my_mean function from Exercise 1 so that it now takes two inputs – a vector of values x, and a vector of weights w – and returns the weighted mean of x with weights w. Hint: If x and w are two vectors of the same length, then x*w is a vector created by multiplying each entry of x with the corresponding entry of w.

my_mean <- function(x, w){
  return(sum(x*w)/sum(w))
}

4. When we calculate a mean, we usually don’t need weights. Modify your my_mean function from Exercise 3 so that the default weights are all 1.

# making the default weights all 1
my_mean <- function(x, w = rep(1, length(x))){
  return(sum(x*w)/sum(w))
}

5. Check that your function from Exercise 4 works:

# should be 2
my_mean(x = c(1, 2, 3))

[1] 2

# should be 2
my_mean(x = c(1, 2, 3), w = c(1, 1, 1))

[1] 2

# should be 1.5
my_mean(x = c(1, 2, 3), w = c(1, 1, 0))

[1] 1.5

Note: You need to make w a vector of the same length as x! The following code will run, but is wrong:

my_mean(x = c(1, 2, 3), w = 1)

[1] 6