The accompanying data file contains 10 observations with three variables, x₁, x₂, and x₃.
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 the three variables. 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 the three variables. Use the minmax transformation to normalize the values, and then compute the Euclidean distance between the first two observations.