Is this a mathematically valid way of determining the mean?

Question

Find the average of 37, 55, and 73. She took 2 from the 37 and gave it to the 73, and 20 from the 73 to give it to the 37 so that all three numbers would now be 55. Is this a mathematically valid way of determining the mean?

Answer 1

Yes. it's mathematically valid.

Let's say you have grades of 85, 89, 88 and 92

What do you need to bring the average up to 90?

take 2 from the 92, give it to the 88, then you just need a 5 and 1 or 6 more to make the 85 and 89 into 90's.

Get a 96 on your next test, and you have an A or 90 average.

It can be a good shortcut to calculate, as well as to check calculations.