Video: AQA GCSE Mathematics Foundation Tier Pack 3 • Paper 2 • Question 11

Ethan spent one week raising money for two charities by painting portraits. (a) He drew this comparative bar chart to show how much money he raised. Write down two mistakes that he made. (b) He wants to work out the median amount raised in the mornings. He calculates (5 + 1)/2 = 3 and concludes that £75 is the median. Is his method correct? Yes or no. Explain your answer. (c) From the money raised, he had to spend £6 each day to cover the cost of his painting materials. And the remainder of the money raised was profit. He decided to give 45% of his profits to charity A and the rest to charity B. Calculate the amount he gave to charity B.

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Video Transcript

Ethan spent one week raising money for two charities by painting portraits. Part a) He drew this comparative bar chart to show how much money he raised. Write down two mistakes that he made.

The table and corresponding bar chart show how much money Ethan raised on Monday, Tuesday, Wednesday, Thursday, and Friday in the morning and in the afternoon. In part a of the question, we were asked to identify two mistakes on the bar chart. The first mistake that has been made is that there is no key. We don’t know whether the grey bars or the black bars represent the amount of money raised in the morning or the afternoon. Whilst it appears at first glance that the grey bars represent the amount of money in the morning and the black bars represent the amount of money raised in the afternoon, we must provide a key to confirm this.

In order to identify the second mistake, we will now look at the heights of the bars and see if they correspond with the numbers in the table. Each square on the vertical axis represents 10 pound. Therefore, half a square would represent five pound. On Monday, the grey bar has a height of 40 and the black bar has a height of 55. These match the numbers in the table.

The heights for Tuesday also match the numbers in the table, 50 pound in the morning and 90 pound in the afternoon. Likewise, the grey bar for Wednesday has a height of 75 and the black bar has a height of 60. Thursday’s bars also match the numbers in the table, 25 and 40. The two bars for Friday do have a height of 95 and 110. However, they have been plotted the wrong way round. For Monday to Thursday, the grey bar represented the amount of money raised in the morning. For Friday, this is 95 pound. It is the black bar that is a height of 95 on the bar chart.

The second mistake is that Friday’s data is plotted inconsistently. The grey bar should have a height of 95, and the black bar should have a height of 110. They are the opposite way around. These are the two mistakes that Ethan made when drawing the comparative bar charts.

The second part of the question says the following. b) He wants to work out the median amount raised in the mornings. He calculates five plus one divided by two is equal to three and concludes that 75 pound is the median. Is his method correct? Tick a box. Yes or no. Explain your answer.

The median value is the middle value when the numbers are placed in ascending order. In this question, the money raised in the morning was 40 pound, 50 pound, 75 pound, 25 pound, and 95 pound. These are not currently in ascending order. Ethan’s first step in order to calculate the median would be to rewrite these in ascending order: 25, 40, 50, 75, and 95.

As there are only five numbers, we can see that the third one will be the middle number, in this case 50 pound. Ethan concluded that the median was 75 pound, which we can clearly see is incorrect. However, in order to get the full marks in this question, we need to understand the method that Ethan has used. He calculated that five plus one divided by two was equal to three. This is because the median or middle term will be the 𝑛 plus one divided by two term.

As there are five days, five plus one divided by two does indeed give us three. Ethan then found the third number in his list, which was Wednesday and 75 pound. Whilst this part of Ethan’s method is correct, as he did not order the data, the median is incorrect.

The final part of the question says the following. c) From the money raised, he had to spend six pound each day to cover the cost of his painting materials. And the remainder of the money raised was profit. He decided to give 45 percent of his profits to charity A and the rest to charity B. Calculate the amount he gave to charity B.

On Monday, Ethan raised a total of 95 pound, as 40 plus 55 is equal to 95. He raised 140 pound on Tuesday, 135 pound on Wednesday, 65 pound on Thursday, and finally 205 pound on Friday. We can therefore calculate the total amount that Ethan raised by adding these five numbers. 95 plus 140 plus 135 plus 65 plus 205 is equal to 640. Therefore, Ethan raised a total of 640 pound.

We’re told that Ethan spent six pound per day on materials. As there were five days, we need to multiply this by five. Six multiplied by five is equal to 30. So Ethan spent a total of 30 pound on materials. We can calculate Ethan’s profit by subtracting this 30 pound from 640 pound. 640 minus 30 is equal to 610. Therefore, Ethan made a profit of 610 pound.

We’re told that he gave 45 percent of this profit to charity A. As percentages must sum to 100, this means that he gave 55 percent of his profit to charity B. 45 plus 55 equals 100. We need to calculate 55 percent of 610. The word “of” in mathematics means multiply. And the word “percent” means out of 100. This means that 55 percent is the same as 0.55 or 55 over 100. We need to multiply this by 610. 0.55 multiplied by 610 is 335.5. This means that the amount of money that Ethan gave to charity B is 335 pound and 50 pence.

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