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S3 Maths: Central Tendency and Data Display (Paper 3: challenge)
S3 Maths: Central Tendency and Data Display (Paper 3: challenge)
S3 maths central tendency paper three, challenge: ten questions on combining groups, solving for a frequency, percentiles and midpoint estimates.
Direct answers Answers in order: 66, 55, 108 degrees, 3, 61, 4, 16.2, 60, about the 10th, and weight by group size.
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)
- FoundationTwenty students average 60 and thirty average 70. What is the mean of all fifty?
- FoundationA data set has mean 50. If every value is multiplied by 1.1, what is the new mean?
- FoundationA category is 30 percent of a pie chart. What is its angle?
- IntermediateScore 2 has 4 students, score 4 has x students and score 6 has 3 students, with mean 3.8. Find x.
- IntermediateForty students average 55 and sixty average 65. What is the mean of the hundred?
- IntermediateWhat is the median of 2, 3, 4, 5 and 100?
- ChallengeFive students score 0 to 9, fifteen score 10 to 19 and ten score 20 to 29. Estimate the mean using midpoints to one decimal place.
- ChallengeTwenty five students average 48. After one leaves, the remaining twenty four average 47.5. What was the leaver score?
- ChallengeIn 40 sorted values, about which value is the 25th percentile?
- Error redoA student says the combined mean is just the average of the two means. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 66 | The totals 1 200 and 2 100 make 3 300, divided by fifty gives 66. |
| 2 | 55 | Multiplying every value by a constant multiplies the mean by the same constant. |
| 3 | 108 degrees | 360 times 0.3 gives 108. |
| 4 | 3 | Solving 26 plus 4x equals 3.8 times (7 plus x) gives x equal to 3. |
| 5 | 61 | The totals 2 200 and 3 900 make 6 100, divided by a hundred gives 61. |
| 6 | 4 | The median takes the middle position and ignores the extreme 100. |
| 7 | 16.2 | The weighted midpoints 4.5, 14.5 and 24.5 total 485, divided by thirty gives 16.2. |
| 8 | 60 | 1 200 minus 1 140 gives 60, so the leaver scored above the mean. |
| 9 | About the 10th | 40 times 0.25 gives 10, so it sits near the tenth value. |
| 10 | You must weight by group size, a plain average fails when sizes differ | The larger group carries more weight, so total score must be divided by total count. |
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.