| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct stem-and-leaf then find median and quartiles |
| Difficulty | Moderate -0.8 This is a straightforward question requiring basic statistical skills: constructing a stem-and-leaf diagram (routine), reading off quartiles from ordered data (simple recall), and a basic probability calculation using combinations. All parts are standard textbook exercises with no problem-solving insight required, making it easier than average. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread5.02b Expectation and variance: discrete random variables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Stem: 14, 15, 16, 17, 18 with values 3 \ | 3 4 5 \ | 1 4 8 8 \ |
| B1 | Correct leaves | |
| Key: \( | 14 | 3\) represents 14300 dollars |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(LQ = 15400\) | B1 [1] | Correct answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\frac{5}{11} \times \frac{4}{10} \times \frac{2}{9} \times 3C2 = \frac{4}{33}\ (0.121)\) | B1 | Mult 3 diff fractions or (5C2 or 2C1) seen in num |
| OR \(\frac{5C2 \times 2C1}{11C3}\) | B1 | Mult by 3C2 o.e. or correct denom |
| B1 [3] | Correct answer |
## Question 4:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Stem: 14, 15, 16, 17, 18 with values 3 \| 3 4 5 \| 1 4 8 8 \| 3 7 \| 5 | B1 | Correct stem |
| | B1 | Correct leaves |
| Key: $|14|3$ represents 14300 dollars | B1 [3] | Key needs dollars |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $LQ = 15400$ | B1 [1] | Correct answer |
### Part (iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{5}{11} \times \frac{4}{10} \times \frac{2}{9} \times 3C2 = \frac{4}{33}\ (0.121)$ | B1 | Mult 3 diff fractions or (5C2 or 2C1) seen in num |
| OR $\frac{5C2 \times 2C1}{11C3}$ | B1 | Mult by 3C2 o.e. or correct denom |
| | B1 [3] | Correct answer |
---4 Prices in dollars of 11 caravans in a showroom are as follows.\\
$\begin{array} { l l l l l l l l l l l } 16800 & 18500 & 17700 & 14300 & 15500 & 15300 & 16100 & 16800 & 17300 & 15400 & 16400 \end{array}$\\
(i) Represent these prices by a stem-and-leaf diagram.\\
(ii) Write down the lower quartile of the prices of the caravans in the showroom.\\
(iii) 3 different caravans in the showroom are chosen at random and their prices are noted. Find the probability that 2 of these prices are more than the median and 1 is less than the lower quartile.
\hfill \mbox{\textit{CAIE S1 2012 Q4 [7]}}