Consider the two datasets from Exercise 16.6. a. Denote the sample medians of the two datasets by Medx and Medy. Is it true that the sample median (Medx +Medy)/2 of the two sample medians is equal to...

Consider the two datasets from Exercise 16.6.

a. Denote the sample medians of the two datasets by Medx and Medy. Is it true that the sample median (Medx +Medy)/2 of the two sample medians is equal to the sample median of the combined dataset with 7 elements?

b. Suppose we have two other datasets: one of size n with sample median Medx and another dataset of size m with sample median Medy. Is it always true that the sample median (Medx + Medy)/2 of the two sample medians is equal to the sample median of the combined dataset with n+m elements? If no, then provide a counterexample. If yes, then explain this.