Average of averages

Let the data be x1, x2, …, xm, and y1, y2, ..., yn.

The average of x is Σxi / m and the average of y is Σyi / n.

The average of x and y is (Σxi + Σyi) / (m+n).

If m = n, we get Σ(xi +yi) / (2n).

In this case, it is the same result as (Σxi / m + Σyi / n) / 2.

If m ≠n, we get (Σxi + Σyi) / (m+n).

In this case, it is different from (Σxi / m + Σyi / n) / 2.