The ACT test makers know that finding the average is probably too easy for most students on the ACT Math section. In order to try to trick you, test makers may throw in something called a weighted average.
In reality, weighted averages are not any more complicated than the plain-ol’ average, and should only slow you down by 10-15 seconds as you rapidly go through a little more number crunching than usual.
We’ll review the concept of averages first, and then head on to tackle weighted averages. The average, also known as the mean, is the sum of a group of numbers divided by the amount of numbers added together.
Definition of the Average for ACT Math
Average = (sum of numbers) / (total amount of numbers)
For example, the average of 3, 3, 5, 6, 4, 2, and 5 is 28/4 or 7.
Definition of Weighted Averages for ACT Math
When some numbers in a group carry more ‘weight’ than other numbers, you need to take that weight into account before plugging the numbers into the formula. This is called a weighted average.
In order to convert the numbers into their weighted counterparts, you need to multiply each number by its weight before adding them together. Also, instead of dividing by the total amount of numbers, you divide by the total weight of the numbers.
You’ll be given the weight of each number, so all you really need to do is figure out which numbers to plug in so that you can get to the answer.
Let’s take a look at this example and break it down step-by-step.
In a class of 2 boys and 3 girls, the boys’ average test score was 75 and the girls’ average test score was 80. What was the average score for the entire class?
Step 1: First we need to recognize that there are an unequal amount of boys and girls. The girls’ scores carry more weight than the boys’ scores, so we need to multiply their scores by their weight.
- Boys’ weighted score = 75*2 = 150
- Girls’ weighted score = 80*3 = 240
- Total weighted score = 150 + 240 = 390
Step 2: We need to find out the total weight to divide by. In this case, there are 2 boys and 3 girls, so the total weight is 5.
Step 3: Now we simply divide the answers we got from number 1 and number 2 to get the solution. 390/5 = 78
Now that you have an understanding of how to solve weighted averages problems, check out our posts on other ACT Math concepts, such as How to Solve Probability Problems and How to Solve Circle Problems.