Exercise 3. Error impact on average

In the previous exercises we saw that the mean and median are very similar and so are the standard deviation and MAD. This is expected since the data is approximated by a normal distribution which has this property.

Now suppose that Galton made a mistake when entering the first value, forgetting to use the decimal point. You can imitate this error by typing:

library(HistData)
data(Galton)
x <- Galton$child
x_with_error <- x
x_with_error[1] <- x_with_error[1]*10

The data now has an outlier that the normal approximation does not account for. Let's see how this affects the average.

Report how many inches the average grows after this mistake. Specifically, report the difference between the average of the data with the mistake x_with_error and the data without the mistake x.