Given the sample dataset of size n = 5: {2, -4, 1, 1, 5x}. Note that x is a real number.
Obtain the empirical influence function for the mean and sketch its influence curve. What does this influence function tell you about the mean (hint: try x = 5 or x =
1,000,000,000,000)? What percent of arbitrary observations could mean tolerate before giving arbitrary results?
Now suppose that x ≥ 1, compute the median. If x = 1, what is the median? If x =
1,000,000,000,000, what is the median? What do you observe regarding the stability of the median for this dataset?