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S3 Maths: Central Tendency and Data Display (Paper 2: intermediate)
S3 Maths: Central Tendency and Data Display (Paper 2: intermediate)
S3 maths central tendency paper two, intermediate: ten questions from frequency table means and weighted means to midpoint estimates.
Direct answers Answers in order: 1.9, 11.5, 22, 67, 14, 26.5, 50.5, 2 790, 7.8, and the median should be used.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S3 Maths: Central Tendency and Data Display |
| Level | S3 |
02 Questions (10 items)
- FoundationScore 1 is held by 4 students, 2 by 3 students and 3 by 3 students. What is the mean?
- FoundationWhat is the median of 3, 5, 6, 8, 9, 11, 12, 14, 15, 16, 18 and 20?
- FoundationWhat is the range of 15, 22, 9, 31 and 18?
- IntermediateHomework 80 with weight 2, test 70 with weight 3 and exam 60 with weight 5. What is the weighted mean?
- IntermediateFive values have mean 8 and after adding one value the six have mean 9. What was added?
- IntermediateWhat is the median of 21, 23, 25, 28, 31 and 34?
- ChallengeEight students score 40 to 49 and twelve score 50 to 59. Estimate their mean using class midpoints.
- ChallengeThe mean score of 45 students is 62. What is their total score?
- ChallengeWhat is the mean of 4, 7, 7, 9 and 12?
- Error redoA student says the mean should replace the median when extreme values appear. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 1.9 | The total 4 plus 6 plus 9 is 19, divided by ten students gives 1.9. |
| 2 | 11.5 | With twelve values, average the sixth and seventh, 11 and 12, to get 11.5. |
| 3 | 22 | The largest 31 minus the smallest 9 gives 22. |
| 4 | 67 | The weighted total 160 plus 210 plus 300 is 670, divided by the total weight 10 gives 67. |
| 5 | 14 | The new total 54 minus the old total 40 gives 14. |
| 6 | 26.5 | With six values, average the middle pair 25 and 28 to get 26.5. |
| 7 | 50.5 | The midpoints 44.5 and 54.5 weighted by 8 and 12 give 50.5. |
| 8 | 2 790 | 62 times 45 gives 2 790. |
| 9 | 7.8 | The total 39 divided by five gives 7.8, while the median is 7. |
| 10 | The median should be used instead, since the mean is dragged away | An extreme value pulls the mean up or down, while the median depends only on position. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Add all values then divide by the count for the mean, always sort before finding the median, trust the median when extreme values appear, and weight by group size when combining two groups.Tutor Registration →
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