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Average · adding one pupil
P6 · Data analysis · PSLE Maths
Question
24 pupils took a Math quiz. Their average score was 76 marks. When Siti's score was included, the average score of the 25 pupils became 76.8 marks. What was Siti's score?
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Hint
First find the original total and the new total using average × number of pupils. The increase in total is Siti's score.
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Answer: Siti's score 96 marks
- Draw the model — For an average question, think of the total score first. At first, there were 24 pupils with an average of 76 marks. After adding Siti, there were 25 pupils with an average of 76.8 marks.
- Original total — Original total = average score × number of pupils. 24 × 76 = 1824, so the total score of the 24 pupils was 1824 marks.
- New total — After adding Siti, there were 25 pupils. The new total score was 25 × 76.8 = 1920 marks.
- Compare totals — The new total = the original total of 24 pupils + Siti's score. So Siti's score is the increase in total: 1920 − 1824 = 96.
- Check — Check: the original total 1824 plus Siti's 96 marks, divided by 25, gives 76.8. So Siti scored 96 marks. 📌 Key idea: when an average changes, find the two totals first. When one pupil is added, new total − original total = the new pupil's score.
Method: For average questions, change the average to a total first: total score = average × number of pupils. After adding one pupil, new total − original total = the new pupil's score.
Practice: 3 similar questions
- The average score of 16 pupils in a Science quiz was 74 marks. When Ali's score was included, the average score of the 17 pupils became 75 marks. What was Ali's score?
Answer
91 marks — Original total = 16 × 74 = 1184 marks. New total = 17 × 75 = 1275 marks. Ali's score = 1275 − 1184 = 91 marks.
- The average score of 22 pupils in an English quiz was 81 marks. When Mei Ling's score was included, the average score of the 23 pupils became 80.5 marks. What was Mei Ling's score?
Answer
69.5 marks — Original total = 22 × 81 = 1782 marks. New total = 23 × 80.5 = 1851.5 marks. Mei Ling's score = 1851.5 − 1782 = 69.5 marks.
- 24 pupils took a Math test marked out of 120. Their average score was 76 marks. Later, when Raju's and Siti's scores were included, the average score of the 26 pupils became 77.5 marks. Raju scored 84 marks. What was Siti's score?
Answer
107 marks — Original total = 24 × 76 = 1824 marks. New total = 26 × 77.5 = 2015 marks. Raju's and Siti's total score = 2015 − 1824 = 191 marks. Siti's score = 191 − 84 = 107 marks.
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