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S5 Maths: Dispersion and Standard Deviation: Paper 2 (Intermediate)
S5 Maths: Dispersion and Standard Deviation: Paper 2 (Intermediate)
Ten items comparing two sets and testing what adding or multiplying by a constant does to mean and spread.
Direct answers Items 1-3: 2, mean 10 with standard deviation 4.24, set E. Items 4-6: mean 15 with standard deviation 2, mean 30 with standard deviation 6, then 4.24. Items 7-9: about 42.4 percent, 9 and 25 percent, 66 marks and 8.8 marks. Item 10: 25.
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 | Intermediate |
02 Questions (10 items)
- FoundationThe data set D is 7, 9, 10, 11, 13. Find its standard deviation.
- FoundationThe data set E is 4, 7, 10, 13, 16. Find its mean and standard deviation (2 d.p.).
- FoundationD and E have the same mean. Which set is more dispersed?
- IntermediateEach value of D is increased by 5. What are the new mean and standard deviation?
- IntermediateEach value of D is multiplied by 3. What are the new mean and standard deviation?
- IntermediateThe variance of E is 18. Find its standard deviation (2 d.p.).
- ChallengeCompare the coefficients of variation of D and E. Which set is relatively more dispersed?
- ChallengeA box-and-whisker diagram shows minimum 2, Q1 = 5, median 9, Q3 = 14 and maximum 20. Find the inter-quartile range and the proportion of values below Q1.
- Challenge40 students score a mean of 60 marks with a standard deviation of 8 marks. If every score rises by 10%, what are the new mean and standard deviation?
- Error redoA set has standard deviation 5, but a student writes its variance as 5. What is the correct variance?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Standard deviation = 2 | The mean is 10, the sum of squared deviations is 20, so the variance is 4 and its square root is 2. |
| 2 | Mean 10, standard deviation 4.24 | The sum of squared deviations is 90, so the variance is 18 and its square root is about 4.24. |
| 3 | Set E | The standard deviation of E is 4.24, which is larger than 2 for D. |
| 4 | Mean 15, standard deviation 2 | Adding a constant shifts the mean only; the gaps between values are unchanged. |
| 5 | Mean 30, standard deviation 6 | Multiplying by k multiplies both the mean and the standard deviation by k. |
| 6 | Standard deviation = 4.24 | Take the square root of the variance: the square root of 18 is about 4.24. |
| 7 | Set E, about 42.43%, against about 20% for D | The coefficient of variation is the standard deviation divided by the mean; both means equal 10. |
| 8 | Inter-quartile range = 9, about 25% | 14 – 5 = 9, and about one quarter of the values lie below Q1. |
| 9 | Mean 66 marks, standard deviation 8.8 marks | Multiplying by 1.1 scales both the mean and the standard deviation by 1.1. |
| 10 | 25 | The variance is the square of the standard deviation, and 5 squared is 25. |
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 →
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