| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Skewness identification and interpretation |
| Difficulty | Easy -1.2 This is a straightforward S1 question requiring basic data handling skills: sorting data into a stem-and-leaf diagram, identifying obvious negative skewness from the shape, and calculating standard measures of location. All techniques are routine recall with no problem-solving or conceptual challenge beyond recognizing a simple pattern. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 29.5\) | B1 | CAO |
| Mean \(= 26.7\) \((26.6666)\) or \(26\frac{2}{3}\) or \(\frac{80}{3}\) or \(26.\dot{6}\) | B1 | CAO — Do not allow 27, but condone 26.6 www |
| Mode \(= 31\) | B1 | CAO |
| The mode is not at all useful as it is just by chance that it is 31. | E1 | Allow any reasonable comment |
# Question 1:
## Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 29.5$ | B1 | CAO |
| Mean $= 26.7$ $(26.6666)$ or $26\frac{2}{3}$ or $\frac{80}{3}$ or $26.\dot{6}$ | B1 | CAO — Do not allow 27, but condone 26.6 www |
| Mode $= 31$ | B1 | CAO |
| The mode is not at all useful as it is just by chance that it is 31. | E1 | Allow any reasonable comment |
**Mark awarded for stating not useful AND:**
- not representative of data
- does not represent Central Tendency
- happened by chance (or similar)
- comment about not appearing significantly more (only one repetition/only twice/ etc)
**No mark for stating it would be useful OR NOT USEFUL because of:**
- spread/range
- sample size
- negatively skewed
- unaffected by outliers
- isn't close to mean and median
**Total: [4]**
---1 At a tourist information office the numbers of people seeking information each hour over the course of a 12-hour day are shown below.
$$\begin{array} { l l l l l l l l l l l l }
6 & 25 & 38 & 39 & 31 & 18 & 35 & 31 & 33 & 15 & 21 & 28
\end{array}$$
(i) Construct a sorted stem and leaf diagram to represent these data.\\
(ii) State the type of skewness suggested by your stem and leaf diagram.\\
(iii) For these data find the median, the mean and the mode. Comment on the usefulness of the mode in this case.
\hfill \mbox{\textit{OCR MEI S1 Q1 [8]}}