Average word problems

Average word problems
Description
Exercise Name:	Average word problems
Math Missions:	High school statistics and probability Math Mission
Types of Problems:	3

The Average word problems exercise appears under the High school statistics and probability 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 user is asked to find the average of the numbers.

   

   Find average of numbers

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 user is asked to find the entire 'weighted average' of the two collections.

   

   Find average with two collections

3. Find score to get average: This problem describes a situation where someone has an average. The user is supposed to find out what needs to be scored to change the overall average to a different given value.

   

   Find score to get average

Strategies

This exercise is easy to get accuracy badges because once users 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 n₁ with average ${a_1}$ and they get another collection of size $n_2$ with average a₂, users simply find ${\frac{(a_1\times n_1+a_2\times n_2)}{(n_1+n_2)}}$.
3. On Find score to get average if users have $n_1$ scores and the average is $a_1$ and users want to raise their average to $a_2$ they should calculate ${a_2\times (n_1+1)-a_1\times n_1}$.

Real-life Applications

1. Businesses can use averages to calculate how much money they make.
2. Data and statistics appear in news reports and in the media every day.
3. Statistics can be seen more frequently than calculus in every day life.