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S3 Maths: Central Tendency and Data Display (Paper 4: mistake clinic)
S3 Maths: Central Tendency and Data Display (Paper 4: mistake clinic)
S3 maths central tendency paper four, mistake clinic: ten questions fixing mean and median confusion, unsorted data and weighting errors.
Direct answers Answers in order: 8, 4, 120, 4, 38, 65, 73.3, 9, 324 degrees, and the data must be sorted first.
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)
- FoundationWhat is the mean of 6, 7, 7, 8 and 12? The median is 7, do not mix them up.
- FoundationWhat is the mode of 3, 4, 4, 5 and 9?
- FoundationEight values have mean 15. What is their total?
- IntermediateWhat is the median of 1, 2, 3, 4, 5, 6 and 7?
- IntermediateWhat is the range of 12, 45, 7 and 30?
- IntermediateSubject A scores 80 with weight 1 and subject B scores 60 with weight 3. What is the weighted mean?
- ChallengeTwenty students average 70 and five of them average 60. What is the mean of the other fifteen, to one decimal place?
- ChallengeWhat is the median of 4, 8, 10 and 14?
- ChallengeA category is 90 percent of a pie chart. What is its angle?
- Error redoA student takes the middle value without sorting first. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 8 | The total 40 divided by five gives 8; mean and median are different measures. |
| 2 | 4 | Four appears twice, more often than any other value. |
| 3 | 120 | The mean times the count gives the total, 15 times 8 is 120. |
| 4 | 4 | With seven values there is a single middle position, the fourth value. |
| 5 | 38 | The largest 45 minus the smallest 7 gives 38. |
| 6 | 65 | The weighted total 80 plus 180 is 260, divided by four gives 65. |
| 7 | 73.3 | The total 1 400 minus 300 leaves 1 100, divided by fifteen gives 73.3. |
| 8 | 9 | With four values, average the middle pair 8 and 10 to get 9. |
| 9 | 324 degrees | 360 times 0.9 gives 324 degrees. |
| 10 | The data must be sorted first, an unsorted middle value is not the median | The median is defined by position after sorting, so an unsorted middle value can be anything. |
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 →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.