It's not just averages, it's division in general. Division is not commutative, as the article says. A simple example referring to the article's diagram of box

It's not just averages, it's division in general. Division is not commutative, as the article says. A simple example referring to the article's diagram of boxes: orders_2013 has sum(price) = 10, with 3 records orders_2014 has sum(price) = 11, with 5 records orders_2015 has sum(price) = 31, with 7 records Average on each node, and average them: ( (10/3)+(11/5)+(31/7) ) / 3 = 3.32063492063 Sum the price individually on each node, take the counts on each node, sum them on the master node, and divide on the master node: (10+11+31)/(3+5+7) = (10+11+31)/15 = 3.46666666667 hence, running division on each node is not the same as finding the division across all orders. (replace my use of division with "average" and it's the same concept).