| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Compare multiple measures numerically |
| Difficulty | Moderate -0.8 This is a straightforward descriptive statistics question requiring only basic calculations (mean, median, midrange) and standard commentary about outliers affecting the mean. No problem-solving or novel insight needed—purely routine application of definitions with minimal computational complexity. |
| Spec | 2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Mean \(= 127.6/13 = 9.8\) | M1, A1 CAO | M1 for \(127.6/13\) soi |
| Median \(= 8.6\) | B1 CAO | |
| Midrange \(= 14.5\) | B1 CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Mean slightly inflated due to the outlier | B1 | |
| Median good since it is not affected by the outlier | B1 | |
| Midrange poor as it is highly inflated due to the outlier | B1 |
# Question 1:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Mean $= 127.6/13 = 9.8$ | M1, A1 CAO | M1 for $127.6/13$ soi |
| Median $= 8.6$ | B1 CAO | |
| Midrange $= 14.5$ | B1 CAO | |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Mean slightly inflated due to the outlier | B1 | |
| Median good since it is not affected by the outlier | B1 | |
| Midrange poor as it is highly inflated due to the outlier | B1 | |
---1 The total annual emissions of carbon dioxide, $x$ tonnes per person, for 13 European countries are given below.
$$\begin{array} { c c c c c c c c c c c c c }
6.2 & 6.7 & 6.8 & 8.1 & 8.1 & 8.5 & 8.6 & 9.0 & 9.9 & 10.1 & 11.0 & 11.8 & 22.8
\end{array}$$
(i) Find the mean, median and midrange of these data.\\
(ii) Comment on how useful each of these is as a measure of central tendency for these data, giving a brief reason for each of your answers.
\hfill \mbox{\textit{OCR MEI S1 2007 Q1 [7]}}