Video: GCSE Mathematics Foundation Tier Pack 4 • Paper 2 • Question 7

GCSE Mathematics Foundation Tier Pack 4 • Paper 2 • Question 7

04:31

Video Transcript

This is a fair spinner with five possible scores. Sam spins the spinner 25 times. The table gives information about the results of his spins. Sam worked out the mean score to be seven. Part a) Explain why it is impossible for the mean score to be seven. There’s also a part b, which we’ll come onto in a bit.

The first thing to do is actually look at some language cause it’s important. The first bit here is this word “fair.” And because it’s a fair spinner, we know it’s equally as likely to land on any of the scores. For part a of this question, we need to look at why it is impossible for the mean score to be seven because Sam worked out the mean as seven.

Well, the reason why it’s impossible for the mean score to be seven is because the maximum score on the spinner is five, which I’ve circled here on the spinner and in the table. And the mean cannot be greater than this because that is impossible. Okay, great, so that’s part a answered. Let’s move on to part b.

Ahmed calculated the mean using the following working. Part b) Explain the mistake that Ahmed made in his calculation.

So in order to actually see what mistake Ahmed has made, what we’re gonna do is actually go through our calculation step by step. We’re gonna start with the first line. The first thing I’ve done is I’ve actually put it in brackets. And this is easier when if we’re entering this into our calculator, it’ll enable us to get the correct answer and also help us to see each stage.

So we can see by the first line what Ahmed is doing is actually multiplying the score by the frequency. So it’s the score by the number of times that actually comes up. Well, this is correct because if we’re wanting to find the total score, which is what we want to find, so the total score when you add up everybody’s score together this will be the correct method.

Now, let’s do the calculation to check that this is correct. So we’ve got one multiplied by six plus two multiplied by five plus three multiplied by four plus four multiplied by three plus five multiplied by seven. Does it equal to 75? Well, what we can do is put it all straight into the calculator and see what the answer is. But what I’ve done is just split it down into each part just to double-check.

So we got six plus 10 plus 12 plus 12 plus 35. Well, if we have these together, we’re gonna get six plus 10 which is 16 plus 12 gives us 28 plus another 12 gives us 40 plus 35 gives us 75. So therefore, the first part of our miscalculation is correct. Let’s move on to the second line.

Well, if we take a look at the second line. We’ve got 75 divided by five which is 15. On the first glance, this is correct because 75 divided by five is in fact 15. However, the five is the issue because we should not be dividing by five. So what we should be doing here is dividing the total score when you add together all the scores by every spin which we did which is 75 by the total number of spins.

Well, we’re not because five is not the total number of spins. 25 would be the total number of spins because it tells us that Sam spins the spinner 25 times. So therefore, the calculation should be in fact 75 divided by 25. So having used this calculation instead, we can then say the third line, so the mean score is 15, must also be incorrect because the mean score is going to be three because 75 divided by 25 is three.

And if we check to see if this is sensible, well, we can have a look at the table and you can see well the score is three. Yes, this is actually a score within the scores we can get because we can get the score one, two, three, four, or five. So it does look like a sensible calculation for the mean.

So therefore, what we can do is explain the mistake that Ahmed made in his calculation. And Ahmed’s mistake was dividing the total sum of the scores by five, as we showed. He should have divided by 25, which is the total number of spins.

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