| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from raw data list |
| Difficulty | Easy -1.8 This is a straightforward data handling question requiring only basic ordering of 10 numbers and application of standard definitions for mode, median, and quartiles. No problem-solving or conceptual understanding is needed—just mechanical application of learned procedures on a small dataset. |
| Spec | 2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(38\) | B1 | |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\text{Median} = 38.5\) | B1 | CAO |
| \(\text{IQR} = 40 - 38\) | M1 | \(39 < UQ < 45 - 36 < LQ \leqslant 38\) |
| \(= 2\) | A1 | If M0 awarded, SCB1 for both \(UQ = 40\) or \(40.5\) and \(LQ = 38\) or \(37.75\) seen |
| Total: 3 |
## Question 1:
**Part (i):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $38$ | **B1** | |
| | **Total: 1** | |
**Part (ii):**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{Median} = 38.5$ | **B1** | CAO |
| $\text{IQR} = 40 - 38$ | **M1** | $39 < UQ < 45 - 36 < LQ \leqslant 38$ |
| $= 2$ | **A1** | If M0 awarded, **SCB1** for **both** $UQ = 40$ or $40.5$ **and** $LQ = 38$ or $37.75$ seen |
| | **Total: 3** | |1 Each of a group of 10 boys estimates the length of a piece of string. The estimates, in centimetres, are as follows.
$$\begin{array} { l l l l l l l l l l }
37 & 40 & 45 & 38 & 36 & 38 & 42 & 38 & 40 & 39
\end{array}$$
(i) Find the mode.\\
(ii) Find the median and the interquartile range.\\
\hfill \mbox{\textit{CAIE S1 2018 Q1 [4]}}