YTread Logo
YTread Logo

What is a Weighted Average?

What is a Weighted Average?
In this video, we're going to talk about

weighted

average

s. We'll talk about

what

a

weighted

average

is,

what

a

weighted

average

means and how to calculate a

weighted

average

. Here's an example where we calculate a

weighted

average

. Let's say that we have a group of kids here, there are five kids, some boys and some girls and for simplicity sake let's just say that each one weighs a hundred pounds. Now one of their father shows up and the father is a bodybuilder. Check out
what is a weighted average
these muscles, check out these eight pack abs, I guess this means the guy has his shirt off which is kind of creepy but anyway he's a big body builder and he weighs 300 pounds. So now we have a group of six people here. The kids 100 pounds each and the father 300 pounds. So now you can ask a question about this group of people, you could say

what

is that

average

weight? We got these two different weights here, 100 pounds and 300 pounds, so you could calculate

what

I call a regular

average

.
You take 100 pounds and 300 hundred pounds because those are the two choices and you add them together and divide by two because they're two different weights. You get 200 pounds and 200 pounds is right smack dab in between 100 and 300. So that's one way that you could get the

average

weight, 200 pounds. But here's the thing, is it really fair to say that the

average

weight of this group is 200 pounds because there are five kids that each weigh 100 pounds and there's only one
father that weighs 300 pounds. So to say that the

average

weight is right in the middle of those two weights kind of doesn't make a lot of sense. It feels like we should be able to take into account the fact that there are many more kids who weigh a lot less than the one bodybuilder father. This is where the idea of a

weighted

average

comes into play. A

weighted

average

takes into account how many things in each group you have. Here's how I would calculate the

weighted

average

in this
group of people, okay? I would take the fact that there are five kids here that weigh 100 pounds each so I do 100 + 100 + 100 + 100 + 100, that's five hundreds for each of the five kids and then I add 300 for the weight of the bodybuilder and I divide by six because there are six things total. Sometimes it's easier to express this with multiplication, I've got five times a hundred plus one times three hundred divided by six because there are six things and when we crank through these
equations we end up with a different answer than this, we end up with the 133 pounds. This is the answer to the

weighted

average

. Now you'll notice this number 133 is much less than 200 and 133 is a lot closer to the weight of the kids. That's because of the

weighted

average

and how it works. The

weighted

average

will pull down the

average

closest to

what

ever we have the most of, okay? So if we're just half and half it would be 200 pounds, we would have the same number of each, but
since we have more of the kids we take that 200 hundred and we pull the number down closer to the weight of

what

we have more of. So that's why the

weighted

average

for here is a 133, very close to the weight of the kids. Now the

weighted

average

could work the other way as well. Let's say that we had a group where four people were 300 pound bodybuilders and there's only one kid that weighed 100 pounds. In that case, we calculate the

weighted

average

. Four 300 pound bodybuilders plus
what is a weighted average
one 100 pound kid divided by five total or we could do this with multiplication (4x300) plus (1x100) divided by five and in that case we get 260 pounds, alright? This number is a lot higher than the number 200 that's right in between and it's much closer to the weight of the bodybuilders. It's much closer to 300 because they're more of the body builders and there's only this one kid. So the

weighted

average

should be closer to the weight of

what

we have more of. Now for

weighted

average

, we don't just have to have two things like the kids and the bodybuilders, we can have a number of different things more than two and we can have a whole bunch of them. In this case I'm talking about a parking lot that has three different kind of cars. They're all called Lemonas because they look like lemons. We got the Lemona G that weighs 3,000 pounds, the Lemona GX that weighs 4,000 pounds and the Lemona GXL which weighs 5,000 pounds. I have a different amounts of
each of them. So how would I calculate the

weighted

average

here?

What

I do is I take the weight of Lemona G, that's 3000 pounds, and I multiply it by how many Lemona G's there are. They're 32 times 3000 pounds each, I take that and then I add the number of GX's. So I've got 5 of them, 5 times 4,000. And then the GXL's, I've got 7 of them, 7 times 5,000 pounds. Now I do this, I've accounted for the weights of each one of these cars and now I've got to divide
by the total number of cars I have in this group and that's 44. So these are the G's, these are the GX's, and these are the GXL's. Do the multiplication of each, add it up, and I'll end up with 3,432 pounds. Now look at how this number compares to weights of the individual cars. This number is closest to the weight of the G and that makes sense because I have a lot more of the Lemona G's than I have of the heavier GX's and GXL's. So this is the

weighted

average

where as the regular

average

for these cars would have been 3,000 plus 4,000 plus 5,000 divided by 3 which would have given us a number that was smack dab in the middle. But once again the

weighted

average

here gives us a number that takes into account how many of each type of these cars I have and gives me a number that is much closer to the type of car that I have the most of. Now a lot of times when you're talking

weighted

average

, you'll have to work with percent so instead of
getting the number of things you'll get the percentages of them like right here. Here's how you calculate a

weighted

average

using percent. Okay,

what

I'm going to do is I'm going to take the weight of the Lemona G here and I'm going to multiply it by 73 percent expressed as a decimal. So the decimal place in 73 percent would be here. To turn this percentage into a decimal I'll have to move the decimal place two spots to the left so I'm going to move it to here
what is a weighted average
to here, okay? The decimal place is going to end up right here. So I'm going to do 0.73 and then multiply that times the weight, 3,000 pounds, and that's the Lemona G. Now for the GX, I'll take 11 percent and express that as a decimal. Move the decimal place two spots the left so it's going to end up here, 0.11 and multiply that times the weight of the GX, 4,000 pounds for that model the car. And finally I'll take 16 percent and express it as a decimal, 0.16 and multiply it
by the weight of the GXL model. Now when you're working with percentages, you don't divide by anything. All you do is multiply the weights by the percentages expressed in decimals and that's all you have to do. This is the same problem as the one that I did before, we're just expressing these abundances or the amount that we have in percent so the answer 3,432 pounds is going to be the same as

what

we got earlier. Anyway, that's how you do

weighted

average

using percent. Now
I have to say this,

weighted

average

doesn't mean that you have to use weights of things, alright? You can calculate a

weighted

average

with the amount of money people make or like how much volume you have and different types of containers, anything you can think of, any measurement you can think of you can do a

weighted

average

of. So I've been using examples of weights here, weights of people, weights of cars but you don't just have to do weights for a

weighted

average

. The only
reason you call it a

weighted

average

is because it takes into account the number of each thing you have and they kind of pull the

average

closest to their value so that's why you call it a

weighted

average

because you give different weight to each type of thing that you have. Finally, if you're interested to see how this equation here is the same as the one that I did here, you can finish this video up and I'll show you at the very end how these are equivalent expressions. So these
two expressions are equivalent ways of writing the calculations for the

weighted

average

for this information here. Let me show you how they're equivalent. We're going to take this and we want to end up with something that looks like this. The first thing we can do is we can see these three different things that are added together on the top of a fraction. We can separate them out, okay? So, I'm going to do 32 times 3,000 divided by 44 plus 5 times 4,000 divided by 44 plus 7 times
5,000 divided by 44, okay? So I can split this into three pieces, each of them have the same denominator. Now take a look at this. I've got a number over 44 in each one of these cases and this is kind of a percentage because 44 is my total, and each one of these numbers in the numerator are fractions of that total. So

what

I can do since these are multiplied together is I can divide this and then just keep it multiplied by that. So 32 divided by 44 gives me 0.73, that's this part, times
3,000 (you can put that in parentheses). Now I can do 5 divided by 44 and that gives me 0.11 and I'm going to multiply this now times 4,000, put that in parentheses, and finally 7 divided by 44 gives me 0.16 times 5,000 and check it out!

What

I end up with when I split these up and I do the division is exactly the same as the number that I get when I take these values and use the straight percentages here. So the point is whether you choose to use the individual numbers of each thing you
have or whether you choose to use the percentages, the way you go about calculating a

weighted

average

has the same math in it. Anyway, now that you know how to calculate a

weighted

average

using the numbers of the things or the percentages of the things, you can now go on and learn how to calculate atomic mass.