# Video: Pack 1 • Paper 1 • Question 7

Pack 1 • Paper 1 • Question 7

03:51

### Video Transcript

Sarah wants to find out how students in her school travel to school. There are 1500 students in her school. She takes a sample of 50 of them. She asks them how they travel to school and records their responses in the table. Work out the number of students in Sarah’s school that you would expect to travel to school by car. Write down any assumptions that you have made and explain how this may affect your answer.

The table shows us that the method of transport of students has car, bus, walk, train and other. And there are 20 students who come by car, 10 students who come by bus, eight students who walk, eight students who come by train, and four students who’ve listed other. So the first stage of the problem is to actually work out the number of students in Sarah’s school that you’d expect to travel to school by car. So we know that the total number of students in the sample is 50 because the question says that and actually if you add up the frequency in the table, that gives us 50. And we’re interested in the number of students who come by car.

So if we look at that table, you can see that actually there are 20 students who come by car. So therefore, we can actually say that the relative frequency, which is another way instead of saying experimental probability, a probability using trials, of a student coming to school by car is equal to 20 out of 50 or twenty fiftieths. And that’s because there are 20 students who said they come by car and there are 50 students in total in the sample. And if we simplify this, we get two-fifths. So that’s great because we now know that actually the probability of relative frequency of a student come by car is two-fifths.

So now, what we need to do is actually see right, how many students would we expect to come by car in the whole school? So we look at the number of students in the whole school and that’s 1500. And in order to actually work out how many students that we would expect to travel to school by car, we can actually use a formula and that formula is that expected outcomes is equal to the probability of an outcome multiplied by the total number. So therefore, in this case, it’s 1500 because that’s the total number of students multiplied by two-fifths because that was the probability of relative frequency for a student travelling by car.

So to actually work this out, what we could do is actually divide 1500 by five, which gives us 300. And then, we got 300 multiplied by two. So therefore, we can say that the number of students in Sarah’s school that you would expect to travel to school by car using the data that we’ve been given would be 600 students. Okay, fab! So that’s the first part answered. Now, we’re gonna move on to the second part.

And the second part of the question actually asks us to write down any assumptions that we’ve made and explain how they would affect our answer. Well, the main key assumption that we’ve made is that the sample is random and unbiased. And therefore, it can be considered as representative of the whole population.

And what we mean by this is that, for instance, if Sarah just asked her class and Sarah happened to be in the sixth form, then there might be more chance that actually a sixth form student would be likely to possibly walk to school on their own or catch the train on their own. However, if you were to ask maybe a younger student, then they might come by car because they’re more likely to be dropped off by parents or it could be anything like this: she could ask only students who’ve actually arrived to school when she was at school, which was early. And that mean actually those students always catch the train because the train is an early train. So many things that could’ve affected it.

So therefore, we do make the assumption that the sample is random and unbiased. And therefore, we can actually consider it as representative of the whole population.