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S5 Maths: Dispersion and Standard Deviation: Paper 1 (Basics)
S5 Maths: Dispersion and Standard Deviation: Paper 1 (Basics)
Ten items on the range, mean, median and quartiles, fixing the basic idea of dispersion first.
Direct answers Items 1-3: 12, 8, 7. Items 4-6: 5, Q3 = 11 with inter-quartile range 6, then 8. Items 7-9: 3.74, the inter-quartile range, range 12 and inter-quartile range 6. Item 10: correct.
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 | Basics |
02 Questions (10 items)
- FoundationThe data set A is 3, 5, 6, 7, 9, 11, 15. Find the range.
- FoundationFind the mean of the data set A.
- FoundationFind the median of the data set A.
- IntermediateFind the lower quartile Q1 of the data set A.
- IntermediateFind the upper quartile Q3 and the inter-quartile range of A.
- IntermediateAnother data set B is 10, 12, 13, 15, 17, 20, 24. Find its inter-quartile range.
- ChallengeThe variance of the data set A is 14. Find its standard deviation (2 d.p.).
- ChallengeWhen two sets are compared for dispersion, which measure is least affected by a single extreme value?
- ChallengeEvery value of the data set A is increased by 100. What are the new range and inter-quartile range?
- Error redoThe standard deviation of a set is 0, so a student claims the range must also be 0. Is the claim correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Range = 12 | Range = largest value – smallest value = 15 – 3 = 12. |
| 2 | Mean = 8 | The seven values add up to 56, and 56 / 7 = 8. |
| 3 | Median = 7 | With seven values in order, the fourth value is the median. |
| 4 | Q1 = 5 | The middle of the lower three values 3, 5, 6 is 5. |
| 5 | Q3 = 11, inter-quartile range = 6 | The middle of the upper three values 9, 11, 15 is 11, and 11 – 5 = 6. |
| 6 | Inter-quartile range = 8 | Q1 = 12 and Q3 = 20, so 20 – 12 = 8. |
| 7 | Standard deviation = 3.74 | The standard deviation is the square root of the variance, and the square root of 14 is about 3.74. |
| 8 | The inter-quartile range | The range uses only the largest and smallest values, so one extreme value can change it a great deal. |
| 9 | Range 12, inter-quartile range 6 | A shift of all values leaves the gaps between them unchanged. |
| 10 | Correct | A standard deviation of 0 means all values are equal, so the range is bound to 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 →
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