中文（繁體）
中文（简体）
English
S5 Maths: Dispersion and Standard Deviation: Paper 4 (Error clinic)
S5 Maths: Dispersion and Standard Deviation: Paper 4 (Error clinic)
Ten items on the usual slips: range confused with the inter-quartile range, a missing square root, extreme values, and n against n – 1.
Direct answers Items 1-3: range 19 with inter-quartile range 6, then 7, then unchanged at 6. Items 4-6: 37.5, the same unit, then unchanged at 2. Items 7-9: 4, unchanged at 6, then 5.00. Item 10: not possible.
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: S5 Maths: Dispersion and Standard Deviation |
| Level | Error clinic |
02 Questions (10 items)
- FoundationThe data set F is 1, 3, 5, 7, 9, 20. Find the range and the inter-quartile range.
- FoundationA set has variance 49. Find its standard deviation.
- FoundationIf 20 in F is changed to 200, what happens to the inter-quartile range?
- IntermediateAfter 20 in F is changed to 200, what is the mean?
- IntermediateHow does the unit of the standard deviation compare with the unit of the data?
- IntermediateEvery value of the data set D (7, 9, 10, 11, 13) is increased by 10. What is the new standard deviation?
- ChallengeA set has standard deviation 2. If every value is multiplied by -2, what is the new standard deviation?
- ChallengeThe median of F is 6. After 20 is changed to 200, what is the median?
- ChallengeA set of 5 values has variance 4 when divided by n. If n – 1 is used by mistake, what is the variance (2 d.p.)?
- Error redoA set has a range of 20 and a standard deviation of 0. Is that possible?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Range 19, inter-quartile range 6 | 20 – 1 = 19; Q3 = 9 and Q1 = 3, a gap of 6. |
| 2 | 7 | The square root of 49 is 7; the variance is not halved. |
| 3 | It stays at 6 | Neither Q1 nor Q3 is affected by an extreme value above them. |
| 4 | 37.5 | The total rises from 45 to 225, and 225 / 6 = 37.5. |
| 5 | It is the same unit | If the data are in cm the standard deviation is in cm; only the variance is in cm squared. |
| 6 | It stays at 2 | Adding a constant leaves the gaps between values unchanged. |
| 7 | 4 | A standard deviation is never negative; 2 x 2 = 4. |
| 8 | It stays at 6 | The median depends on position only, so an extreme value does not move it. |
| 9 | 5 | The sum of squared deviations is 20, and dividing by 4 gives 5, a larger figure. |
| 10 | Not possible | A standard deviation of 0 means all values are equal, so the range must be 0. |
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.
Write the mean first, then list each squared deviation; that keeps the working clean.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.