Question

what is the average(arithmetic mean) of the positive integers from 1 to 50 inclusive?

Answer 1

add up all the number between 1 and 50 (including 1 and 50) and then divide that amount by how many digits are between 1 and 50(inculsive)

Answer 2

Isn't there a shortcut?

Answer 3

this is a PSAT question by the way

Answer 4

here is what you do: google: shortcut for arithmitec mean

Answer 5

after you do that, go play pokemon

Answer 6

Think about it logically:

1 + 50 = 51
2 + 49 = 51
3 + 48 = 51
...
25 + 26 = 51

These 25 pairs of numbers all equal 51 - If you add them all together, you'd be multiplying 51 by 25, then dividing by 50 to get the average.

So, you're multiplying 51 by (25/50) or taking:
\[\frac{1 }{ 2 }*50\]

The answer is 25.5.