| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2004 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Removing data values |
| Difficulty | Moderate -0.3 This is a straightforward application of formulas for mean and standard deviation with a removal scenario. Part (i) requires direct calculation from summary statistics. Part (ii) involves simple algebra to find the removed value (745 - 17×41 = 48) and recalculating standard deviation. While it requires careful arithmetic and understanding of how summary statistics change, it's a standard textbook exercise with no conceptual challenges beyond routine manipulation of formulas. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Mean \(= 745/18 = 41.4\) | B1 | For correct answer, a.e.f. |
| \(\text{sd} = \sqrt{\frac{33951}{18} - \left(\frac{745}{18}\right)^2}\) | M1 | For \(\sqrt{[33951/18 - (\text{their } 41.4)^2]}\) or \(\div 17\) |
| \(= 13.2\) | A1 3 | For correct answer; 13.1 gets A0 with PA #1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(17 \times 41 = 697\) | M1 | For multiplying 17 by 41 |
| \(745 - 697 = 48\) | A1 2 | For correct answer |
| \(\text{sd} = \sqrt{\frac{33951 - 48^2}{17}} - 41^2 = 13.4\) | M1 | For subtracting *their* \(48^2\) from 33951 (ignore anything else) |
| A1 2 | For correct answer |
# Question 4:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Mean $= 745/18 = 41.4$ | B1 | For correct answer, a.e.f. |
| $\text{sd} = \sqrt{\frac{33951}{18} - \left(\frac{745}{18}\right)^2}$ | M1 | For $\sqrt{[33951/18 - (\text{their } 41.4)^2]}$ or $\div 17$ |
| $= 13.2$ | A1 **3** | For correct answer; 13.1 gets A0 with PA #1 |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $17 \times 41 = 697$ | M1 | For multiplying 17 by 41 |
| $745 - 697 = 48$ | A1 **2** | For correct answer |
| $\text{sd} = \sqrt{\frac{33951 - 48^2}{17}} - 41^2 = 13.4$ | M1 | For subtracting *their* $48^2$ from 33951 (ignore anything else) |
| | A1 **2** | For correct answer |
---4 The ages, $x$ years, of 18 people attending an evening class are summarised by the following totals: $\Sigma x = 745 , \Sigma x ^ { 2 } = 33951$.\\
(i) Calculate the mean and standard deviation of the ages of this group of people.\\
(ii) One person leaves the group and the mean age of the remaining 17 people is exactly 41 years. Find the age of the person who left and the standard deviation of the ages of the remaining 17 people.
\hfill \mbox{\textit{CAIE S1 2004 Q4 [7]}}