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
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
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
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.