# Weighted Average when adding and removing items

This might be a silly question for you guys, but I've been struggling myself to handle it. Imagine we have a fish tank with:

• number of fishes: 1000
• weighted average: 0.233 (kg)

One day, I decided to remove 200 fishes having 0,5 kg of weighted average. What would be the new weighted average and how to calculate it?

On adding operations, I handle it as follows (using the same example):

((1000 * 0.233) + (200*0.5))/(1000+200), resulting 1 kg.

Any help will be really appreciated!

Thanks!

• What do you mean by weighted average? Is this maybe only about the average weight? – Jasper May 26 '18 at 7:23
• Review the definition of the weighted average. – NoChance May 26 '18 at 8:48
• @jasper yes. The weighted average per fish. On addition example is 1kg – hugalves May 26 '18 at 14:51

Okay so the total weight before you removed the 200 fishes was $0.233\cdot 1000=233$ kg. The removed 200 fish have a total weight $200*0.5=100$ kg. This leaves in the box 800 fishes with a weight of 133 kg, so the average weight of the fishes inside the box is $\frac{133}{800}=0.166$ kg.

• I guess the OP is not asking about the average weight per fish, instead they are asking about "What would be the new weighted average". – NoChance May 26 '18 at 6:58