{"id":7667,"date":"2016-08-23T10:22:23","date_gmt":"2016-08-23T17:22:23","guid":{"rendered":"https:\/\/magoosh.com\/act\/?p=7667"},"modified":"2018-09-24T20:51:34","modified_gmt":"2018-09-25T03:51:34","slug":"act-math-weighted-averages-problems","status":"publish","type":"post","link":"https:\/\/magoosh.com\/act\/act-math-weighted-averages-problems\/","title":{"rendered":"ACT Math: How to Solve Weighted Averages Problems"},"content":{"rendered":"

The ACT test makers know that finding the average is probably too easy for most students on the ACT Math<\/a> section. In order to try to trick you, test makers may throw in something called a weighted average.<\/p>\n

In reality, weighted averages are not any more complicated than the plain-ol\u2019 average, and should only slow you down by 10-15 seconds as you rapidly go through a little more number crunching than usual.<\/p>\n

We\u2019ll review the concept of averages first, and then head on to tackle weighted averages.\u00a0The average, also known as the mean, is the sum of a group of numbers divided by the amount of numbers added together.<\/p>\n

Definition of the Average for ACT Math<\/h2>\n

Average = (sum of numbers) \/ (total amount of numbers)<\/strong><\/p>\n

For example, the average of 3, 3, 5, 6, 4, 2, and 5 is 28\/4 or 7.<\/p>\n

Definition of Weighted Averages for ACT Math<\/h2>\n

\"ACT<\/p>\n

When some numbers in a group carry more \u2018weight\u2019 than other numbers, you need to take that weight into account before plugging the numbers into the formula. This is called a weighted average.<\/p>\n

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.<\/p>\n

You\u2019ll 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.<\/p>\n

Let\u2019s take a look at this example and break it down step-by-step.<\/strong><\/p>\n

In a class of 2 boys and 3 girls, the boys\u2019 average test score was 75 and the girls\u2019 average test score was 80. What was the average score for the entire class?<\/em><\/p>\n

Step 1: First we need to recognize that there are an unequal amount of boys and girls. The girls\u2019 scores carry more weight than the boys\u2019 scores, so we need to multiply their scores by their weight.<\/p>\n