Consider two datasets: 1, 5, 9 and 2, 4, 6, 8. a. Denote the sample means of the two datasets by ¯x and ¯y. Is it true that the average (  + )/2 of and  is equal to the sample mean of the combined...

Consider two datasets: 1, 5, 9 and 2, 4, 6, 8. a. Denote the sample means of the two datasets by ¯x and ¯y. Is it true that the average ( +
)/2 of
and
 is equal to the sample mean of the combined dataset with 7 elements? b. Suppose we have two other datasets: one of size n with sample mean x¯n and another dataset of size m with sample mean ¯ym. Is it always true that the average (xn + ym)/2 of ¯xn and ¯ym is equal to the sample mean of the combined dataset with n + m elements? If no, then provide a counterexample. If yes, then explain this. c. If m = n, is (xn+ ym)/2 equal to the sample mean of the combined dataset with n + m elements?