Three different toys are stored in a warehouse. There are 15000 toys in total and the number of each is shown in the table. A stratified sample of all the toys is taken and 420 cars are selected. Calculate the total number of toys in the sample.
To answer this question, we first need to look at this term: stratified sample. We’ll have to have a look at what is a stratified sample. One way that we can think about it is that the stratified sample size of a group is proportional to the number of items in that group. So what does that mean in practice? Well, I’ll show you a little formula that can help us. Well, we can say that the stratified sample size is equal to the group size over the total population multiplied by the sample size.
So now let’s have a look at what the question is asking us to find. Well, the question is asking us to find the total number of toys in the sample. Well, in order to do this, so we obviously want to find the sample size, we can actually substitute in the values we have for the rest of our formula. So first of all, we’ve got the stratified sample size which is 420. And that’s gonna be equal to 7000 — because there are 7000 cars cause it’s cars that we’re looking at, so that’s our group size — divided by our total population, so that’s all of our toys which is 15000, multiplied by our sample size which is what we’re trying to find.
Okay, now we can rearrange this to find our sample size. So in order to do that, we’re gonna divide both the sides by 7000 over 15000. So we’ve now got 420 divided by 7000 over 15000 is equal to our sample size. And now we can calculate this to get our sample size. So therefore, we can say that our sample size is equal to 900 toys. So that means that we’ve got a sample size of 900 toys. And we know that 420 of those toys in our sample are going to be cars.
Then we always like to do a little check and see. Is the answer sensible? Well, let’s think about it. We have a sample size of 900 toys. And we have 420 of those toys are going to be cars. Remember, a stratified sample is one that is in proportion. Well, if we look at the total number of different types of toys, we’ve got 2000 bears, 6000 dolls, and 7000 cars. Well, actually 7000 is-is the most there. And we know that 420 is actually the largest part of the 900 toys because then you’ve got 480 toys to share between the other two. So yes, it seems like a sensible answer. If your answer was greater than 900 or with a small portion, then we could know there’s something wrong with the calculation. So yeah, we’ve checked it. We’re happy. So we can agree and say that yes, the sample size is equal to 900 toys.