Question

The average (arithmetic mean) of the 13 numbers in a list is 40. If the average of 11 of the numbers in the list is 21, what is the average of the other two numbers?

Answer 1

average = (sum of items) / (# of items)

if you multiply both sides by # of items, you get

sum of items = average * (# of items)

so if a list has 13 items and average of 40, it's sum is 40 * 13

now, it also tells that 11 numbers (taken from the original 13) has an average of 21, so repeat the logic from before to calculate the sum of these 11 items.

finally, subtract (sum of the 13 items) - (sum of the 11 items) to get the sum of the last 2 items. divide by 2 to get the average.

Answer 2

I understand but I'm curious – why are we subtracting and then dividing by 2?

Answer 3

in order to get the average of the last 2 items, we need to know the sum of the 2 items, and then divide by 2 to get the average.

in order to get the sum of the last 2 items, you need to subtract (sum of all 13 items) - (sum of 11 items) = (sum of the last 2 items)

if you're still confused, think about it backwards

(sum of the first 11 items) + (sum of the last 2 items) = (sum of all 13 items)

Answer 4

How can I further learn about this? What do you suggest?

Answer 5

well this problem really only uses one main concept: the average formula, which you'll simply have to memorize.

mathisfun and khan academy are good beginner friendly websites to learn math concepts like this

Answer 6

Thank you!