Average word problems

The first instance of  is under the Probability and statistics Math Mission. This exercise uses the arithmetic mean to find the answer to story problems.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find average of numbers: This problem just lists a collection of scores. The student is asked to find the average of the numbers.AVWP1.png
 * 2) Find average with two collections: This problem says that a certain collection of exams has a certain average and then an additional collection of tests are performed with scores. The student is asked to find the entire 'weighted average' of the two collections.AVWP2.png
 * 3) Find score to get average: This problem describes a situation where someone has an average. The student is supposed to find out what needs to be scored to change the overall average to a different given value.AVWP3.png

Strategies
This exercise is easy to get accuracy because once you understand how to calculate a problem, all similar problems can be done in the same way. Speed badges are easy because the calculations do not take more than a couple steps.
 * 1) On Find the average of numbers the calculation is just to add them up and divide by how many there are.
 * 2) On Find average with two collections, if the first population is n_1 with average a_1 and you get another collection of size n_2 with average a_2, you simply find $$(a_1\times n_1+a_2\times n_2)/(n_1+n_2)$$.
 * 3) On Find score to get average if you have n_1 scores and the average is a_1 and you want to raise your average to a_2 you should calculate $$a_2\times (n_1+1)-a_1\times n_1$$.