Video: AQA GCSE Mathematics Higher Tier Pack 3 • Paper 2 • Question 10

The UK is home to black, red, and grey squirrels. A biologist collects some data on the number of squirrel sightings in the north and the south of the UK. She records that 4% of squirrels sighted in the north of the UK were black. The following table shows her results for the south of the UK. The biologist claims that the percentage of squirrels that are black is greater in the south of the UK than in the north of the UK. Comment on the biologist’s claim. You must show your working.

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Video Transcript

The UK is home to black, red, and grey squirrels. A biologist collects some data on the number of squirrel sightings in the north and the south of the UK. She records that four percent of squirrels sighted in the north of the UK were black. The following table shows her results for the south of the UK. There were 24 sightings of black squirrels and 320 sightings of red or grey squirrels. The biologist claims that the percentage of squirrels that are black is greater in the south of the UK than in the north of the UK. Comment on the biologist’s claim. You must show your working.

So we’re told that four percent of the squirrels in the north are black. But she’s claiming that the percentage of black squirrels in the south is actually greater than the four percent that are found in the north. We need to comment on this claim. So we must find the percentage of black squirrels in the south. So we need to use this table.

In order to find the percentage, we first need to find the total number of squirrels that are in the south. So we need to take the 24 black squirrels plus the 320 red or grey squirrels. So there are a total of 344 squirrels in the south of the UK. So to find the percentage of black squirrels in the south of the UK, we need to take the number of black squirrels that were sighted, which was 24, and put it out of the total 344.

However, we want a percent. So we need to multiply by 100. Because when we take 24 divided by 344, we get around 0.0698. And like we said, to get a percentage, we need to multiply this number by 100. So the percentage of black squirrels in the south of the UK will be 6.98 percent.

So based on the two samples, the biologist is correct. 6.98 percent is greater than four percent. So the percentage of blacks squirrels in the south is greater than the percentage of black squirrels in the north. However, we don’t know if the two samples are fair and therefore representative of the whole population and, hence, may not be correct.

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