Statistics Question re: Mean

[Jonathan Whatley]

Let's answer an easier question that's really close. That'll give us the skeleton of an equation we can use to solve the question asked.

The mean of a set of 10 numbers is 40, the mean of a set of 30 numbers is 60, and the mean of a set of 60 numbers is 1. What is the mean of these 100 numbers?

( (10 numbers * 40) + (30 numbers * 60) + (60 numbers * 1) ) / 100 numbers total = x = 22.6

Now, instead of plugging in that 1 and solving for the mean, let's plug in the mean and solve for the value we just pretended was 1, the mean of that set of 60.

(The equation above was algebra, we just probably don't think of it as algebra because the unknown x is on its own on the right after the equal sign. It was really easy algebra. The next part is slightly less easy algebra, but still pretty easy!)

( (10 numbers * 40) + (30 numbers * 60) + (60 numbers * x) ) / 100 = 34
( 400 + 1800 + 60x ) / 100 = 34
2200 + 60x = 3400
60x = 1200
x = 20

To check our work, let's plug in 20 in place of x and, yep!, the mean of that whole set of numbers is 34.