**Weighted Average GMAT Problems [video]**

Weighted Average GMAT Questions is definitely one area where you need to prepare. Watch the video below to get introduced to the topic and how you can ace weighted average questions in the GMAT.

## Weighted Average GMAT Questions [Transcript]

In this lesson, we will learn how to calculate weighted averages and we will learn some general properties of weighted averages. To set this up, consider the following: Let’s say we have six men and their average age is twenty. And we have six women and their average age is forty. Now, what happens if we combine these two groups? What will be the average age of the combined population? Well if you said thirty, you’re right. To see why, let’s find the sum of the ages of the men and the sum of the ages of the women. To do this, we will use the following formula. So since the average age of the men is 20 and there are 6 men altogether, the sum of their ages will be 20 X 6, which is 120. When we apply the same formula to the population of women, we see that the sum of their ages is 240.

Now let’s see what happens when we combine both populations. The average age of these 12 people will be the sum of all 12 ages divided by 12. So the sum of the men’s ages is 120 and the sum of the women’s ages is 240. We will now divide this by 12. When we simplify this, we get an average of 30. Notice that the average age of the combined population is equal to the average of the average ages of the two original groups. Okay, now let’s take the original question and change it slightly. Let’s keep the average ages of the men and women at 20 and 40 respectively. But let’s remove 4 of the men. Now if we combine the two groups, what will be the average age of the combined population? To determine this, let’s take the two original groups and find the sum of their ages. Once again, we will apply this formula. For the men, the average age is 20 and there are now 2 men. So the sum of their ages will be 20 X 2, which is 40. When we apply the same formula to the women, we see that the sum of their ages is 240. Now, when we combine the two groups, the average age of the 8 people will be the sum of all 8 ages divided by 8. The men’s ages add to 40 and the women’s ages add to 240. So the average age of the combined population is 35. Notice that this time the average age of the combined population is not the same as the average of the average ages of the two original groups.

Okay. Now let’s look at a different way to find the average age of the combined population. To do this, we need to recognize that the average age of the entire population depends on the proportion of men in the group and the proportion of women in the group. Now, in this population of 8 people, we have 2 men. So the men comprise 2/8ths of the combined population. At this point, we’ll take this fraction and multiply it by the average age of the male population, which is 20. Now to this calculation, we will add the contribution of the female population. So in the combined group of 8 people, we have 6 women. So the women comprise 6/8ths of the combined population. We will now multiply this by the average age of the female population, which is 40. Now when we simplify this, we see that the average age of the combined population is still 35. We can now take these results and generalize them as follows.

If we are combining two or more groups where we know the average of each individual group, then to find the weighted average of the combined population, we will take the proportional representation of one group, say group A, and multiply it by the average of that group. Then we will do the same for another group and so on. Okay, now let’s apply this formula to the following question. Here we have three classes of Calculus 101. Class A has 20 students, class B has 30 students, and class C has 50 students. We are given the average test scores for each class and we want to determine the average score for all three classes combined. Since there is a different number of students in each class, we can use the weighted average formula. So first, let’s determine the total number of students in the combined population. When we add the populations of each class, we get a total population of 100.

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