| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2017 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from raw data |
| Difficulty | Easy -1.2 This is a straightforward application of mean and standard deviation definitions to simple arithmetic contexts. Part (i) requires setting up and solving a basic linear equation from the mean formula. Part (ii) tests understanding that zero standard deviation implies all values are equal, leading to immediate arithmetic. Both parts involve only routine recall and elementary algebra with no problem-solving insight required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(4 \times 5.5 + 3x + 90 = 8 \times 29\) | M1 | An expression to work out total cost of individual items \(= 8 \times\) mean, \(x\) may be implied |
| \(112 + 3x = 232\), \(x = 40\) | A1 | Correct complete unsimplified expression/calculation |
| Cost \(= \\)40$ | A1 | Units not required |
| Total: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\text{sd} = 0\) so all cost the same | M1 | Must see comment interpreting \(\text{sd} = 0\), OE |
| Shirts cost \(4 \times \\)26 = \\(104\) AG | A1 | See \(4 \times \\)26\(, \)\\(130 - \\)26\( OE. Must have final value of \)\\(104\) stated |
| Total: 2 |
## Question 1(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| $4 \times 5.5 + 3x + 90 = 8 \times 29$ | M1 | An expression to work out total cost of individual items $= 8 \times$ mean, $x$ may be implied |
| $112 + 3x = 232$, $x = 40$ | A1 | Correct complete unsimplified expression/calculation |
| Cost $= \$40$ | A1 | Units not required |
| **Total: 3** | | |
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## Question 1(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\text{sd} = 0$ so all cost the same | M1 | Must see comment interpreting $\text{sd} = 0$, OE |
| Shirts cost $4 \times \$26 = \$104$ **AG** | A1 | See $4 \times \$26$, $\$130 - \$26$ OE. Must have final value of $\$104$ stated |
| **Total: 2** | | |
---1 Rani and Diksha go shopping for clothes.\\
(i) Rani buys 4 identical vests, 3 identical sweaters and 1 coat. Each vest costs $\$ 5.50$ and the coat costs $\$ 90$. The mean cost of Rani's 8 items is $\$ 29$. Find the cost of a sweater.\\
(ii) Diksha buys 1 hat and 4 identical shirts. The mean cost of Diksha's 5 items is $\$ 26$ and the standard deviation is $\$ 0$. Explain how you can tell that Diksha spends $\$ 104$ on shirts.\\
\hfill \mbox{\textit{CAIE S1 2017 Q1 [5]}}