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AQA GCSE · Question 14 · Statistics

PearBananaAppleOther48°78°

Some people were asked to choose their favourite fruit. The pie chart shows information about the results. 120 people chose Banana. How many people chose Apple?

How to approach this question

1. Find the angle for the Banana sector. The total angle in a circle is 360°. The other angles are 90° (for Pear, indicated by the square symbol), 48° (Apple), and 78° (Other). 2. Angle for Banana = 360° - 90° - 48° - 78° = 144°. 3. We are told that 120 people correspond to the Banana sector, which is 144°. 4. Find out how many people are represented by one degree: 120 people / 144° = 5/6 people per degree. 5. The angle for Apple is 48°. 6. Calculate the number of people who chose Apple: 48° * (5/6 people/degree). 7. Number of people for Apple = 40. Alternatively: 1. Find the angle for Banana (144°). 2. Set up a proportion: (people for Apple) / (angle for Apple) = (people for Banana) / (angle for Banana). 3. Let x be the number of people who chose Apple. x / 48° = 120 / 144°. 4. Solve for x: x = 120 * (48 / 144) = 120 * (1/3) = 40.

Full Answer

40 people
Step 1: Find the angle for the Banana sector. A pie chart represents a full circle, which is 360°. The angle for Pear is indicated by the square symbol, which means it is a right angle, 90°. The other given angles are 48° for Apple and 78° for Other. Angle for Banana = 360° - (Angle for Pear + Angle for Apple + Angle for Other) Angle for Banana = 360° - (90° + 48° + 78°) Angle for Banana = 360° - 216° Angle for Banana = 144° Step 2: Find the number of people per degree. We are told that 120 people chose Banana, which corresponds to an angle of 144°. People per degree = 120 people / 144° = 5/6 Step 3: Calculate the number of people who chose Apple. The angle for Apple is 48°. Number of people for Apple = Angle for Apple × People per degree Number of people for Apple = 48° × (5/6) Number of people for Apple = (48 × 5) / 6 = 240 / 6 = 40. So, 40 people chose Apple.

Common mistakes

✗ Not recognising the 90° angle for Pear. ✗ Making an error when calculating the angle for Banana. ✗ Incorrectly setting up the proportion or scaling factor. ✗ Dividing 144 by 120 instead of 120 by 144.

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