The accompanying data file contains 10 observations with two variables, x₁ and x₂.
a. Using the original values, compute the Euclidean distance between the first two observations.
b. Using the original values, compute the Manhattan distance between the first two observations.
c. Based on the entire data set, calculate the sample mean and standard deviation for x₁ and x₂. Use z-scores to standardize the values, and then compute the Euclidean distance between the first two observations.
d. Based on the entire data set, find the minimum and maximum values for x₁ and x₂. Use the min-max transformation to normalize the values, and then compute the Euclidean distance between the first two observations.