Partial Means
From the mean of 64 numbers, and the mean of the first 36 of these numbers, can you work out the mean of the last 28 numbers?
Age
14 to 16
Challenge level
Problem
The mean of a sequence of $64$ numbers is $64$.
The mean of the first $36$ numbers is $36$.
What is the mean of the last $28$ numbers?
Student Solutions
The sum of all $64$ numbers is their mean times the number of numbers, which is $$64 \times 64 = 4096$$
Similarly the sum of the first $36$ numbers is $$36 \times 36 = 1296$$
Therefore the sum of the last $28$ numbers is $$4096 - 1296 = 2800$$
Therefore the mean of the last $28$ numbers is $$\frac{2800}{28}=100$$