Video: Pack 1 • Paper 3 • Question 16

Pack 1 • Paper 3 • Question 16

03:22

Video Transcript

The histogram below shows information about the number of words per article written by a new local newspaper. The newspaper has written 1065 articles in total. 15 percent of the articles between 200 and 350 words are written in the technology section of the newspaper. Work out an estimate for the number of technology articles between 200 and 350 words.

In a histogram, the area of each bar represents its frequency. Each bar is a rectangle. So the frequency can be found by multiplying its width by its height or its frequency density. Let’s start then by finding the total frequency of the articles with between 200 and 350 words.

We will need to do this in two parts by first considering the number of articles with between 200 and 300 words, represented by this shaded bar. Remember the frequency is given by the area of each bar. Its width is 100 and its height is 3.4. We can interpret this scale by recognising that 10 little squares is equal to one on the frequency density scale. This means that one little square must be equal to 0.1. The top of the bar sits four little squares above the number three, which means it must have a height of 3.4. This means that there are 340 articles with between 200 and 300 words.

Next, we need to calculate the number of articles with between 300 and 350 words. That’s just a portion of this larger bar. The width of the bar shaded is 50. And once again, using a scale that one little square is equal to 0.1, we can see that the height of this bar is 1.6. There are, therefore, 80 articles with between 300 and 350 words.

Adding these two numbers together, we can see the total number of articles with between 200 and 350 words is 420. We are told that 15 percent of these articles are written in the technology section. We, therefore, need to find 15 percent of 420. There are a number of different ways we can perform this calculation. If we were in a noncalculator paper, we could start by finding 10 percent of 420 by dividing by 10. This gives us 42. Next, we halve this number to get five percent of 420 is equal to 21. Adding these together gives us 15 percent of 420 is equal to 63.

Alternatively, we know that percent means out of 100. So we could work out 15 divided by 100 multiplied by 420 or we could even convert 15 out of 100 into a 0.15. Each of these calculations will give you the exact same answer.

An estimate for the number of technology articles between 200 and 350 words is, therefore, 63.

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