| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Construct stem-and-leaf then find median and quartiles |
| Difficulty | Easy -1.2 This is a straightforward data handling question requiring basic statistical skills: constructing a stem-and-leaf diagram (a routine S1 task), identifying skewness visually, and calculating standard measures of location. All techniques are direct applications with no problem-solving or conceptual challenges beyond recall and careful arithmetic. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Stem-and-leaf diagram with stems 0,1,2,3 and correct leaves | G1 | Stem (either order) and leaves. Do not allow leaves 21, 25, 28 etc. Ignore commas between leaves |
| Sorted and aligned | G1 | Allow errors in leaves if sorted and aligned |
| Key: \(1 \mid 8\) represents 18 people | G1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Negative | B1 | Allow -ve but NOT skewed to the left. Do not allow 'negative correlation' |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median \(= 29.5\) | B1 | CAO |
| Mean \(= 26.7\) (\(26.6\overline{6}\) 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: not representative of data, does not represent central tendency, happened by chance, only one repetition. No mark for spread/range, sample size, negatively skewed, unaffected by outliers, isn't close to mean and median |
## Question 5:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Stem-and-leaf diagram with stems 0,1,2,3 and correct leaves | G1 | Stem (either order) and leaves. Do not allow leaves 21, 25, 28 etc. Ignore commas between leaves |
| Sorted and aligned | G1 | Allow errors in leaves if sorted and aligned |
| Key: $1 \mid 8$ represents 18 people | G1 | |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Negative | B1 | Allow -ve but NOT skewed to the left. Do not allow 'negative correlation' |
### Part (iii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Median $= 29.5$ | B1 | CAO |
| Mean $= 26.7$ ($26.6\overline{6}$ 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: not representative of data, does not represent central tendency, happened by chance, only one repetition. No mark for spread/range, sample size, negatively skewed, unaffected by outliers, isn't close to mean and median |
---5 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 2015 Q5 [8]}}