Video: GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 14

GCSE Mathematics Foundation Tier Pack 5 • Paper 1 • Question 14

04:56

Video Transcript

A group of students were asked about their favourite genre of fiction novels. The table shows the results of male and female students. Part a) says, “Draw a comparative bar chart on the grid to show this information.” Part b) says, “Work out the percentage of the total number of students who were female.”

Let’s take a look at the table. It says that it shows result of male and female students. The male results show in this row and the female results are shown in this row. We can see that four males and four females chose fantasy as their favourite genre of fiction novels. There were five males and two females who chose action and adventure, two males and two females chose crime fiction, and one male and five females chose romance as their favourite genre of fiction novels.

So part a) wants us to draw a comparative bar chart. So we want to draw a bar chart that will compare the male and females. So let’s create a key in the top right-hand corner. We will have the male bars be striped and the female bars be polka dot. We will put the different genres down on the bottom, which we could call the 𝑥-axis. On the 𝑦-axis, we have our numbers one, two, three, four, five, and six.

And we purposely chose to arrange them this way because we wanna make sure that we can get to at least five because that’s the most that was found in any of the rows, five. So each small box represents a half.

So let’s begin with fantasy. Four males chose fantasy and four females chose fantasy. So here would be the bar for males and here would be the bar to represent females who chose fantasy. Now, for action and adventure, five males chose this as their favourite genre, while only two females chose this as their favourite genre. There were two males and two females who chose crime fiction as their favourite, while only one male chose romance as their favourite. But we had five females who chose romance as their favourite.

So the nice thing about this comparative bar chart is that it’s very easy to compare how many or around about how many students picked the genre based on whether they are male or female. So fantasy and crime fiction both had the exact same amount of male and female students who choose that, where for action and adventure and the romance section, it definitely differed between the male and female. So using this, it’s easy to compare them at a glance.

Now, for part b), it says work out the percentage of the total number of students who were female. So we need to come up with some totals. This block will represent the total number of males. So we need to add four plus five plus two plus one. So we find that the total number of males was 12.

Now, let’s do this for females: four plus two plus two plus five. So the total number of females will be 13. Now, to have the total of both male and female, we can place here. So we need to add 12 and 13. So this means altogether, there were 25 students.

And we want to know the total number of students who were female and we want this as a percentage. And the way to do this is to take the number of female students and put it over the total number of students. The total number of female students was 13 and the total number of students altogether was 25.

Now, we don’t want this as a fraction we want it as a percentage. And a percent is out of 100. So how could we get our denominator to change so that way it’s equal to 100? Well, we would need to multiply by four. And whatever we would do to the denominator, we must also do to the numerator. And 13 times four is 52, so 52 out of 100. That is equal to 52 percent.

So here for part a), we created our comparative bar chart and for part b) we found that the percentage of the total number of students who were female would be 52 percent, so a little over half.

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