| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.8 This is a straightforward S1 question requiring only basic reading of a stem-and-leaf diagram and finding median/quartiles by counting positions (no calculation needed). The conceptual questions in parts (ii) and (iii) ask for standard textbook responses about when to use median vs mean and comparing diagram types—pure recall with no problem-solving. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02i Select/critique data presentation |
2 The back-to-back stem-and-leaf diagram below shows the number of hours of television watched per week by each of 15 boys and 15 girls.
$$\begin{aligned}
& \text { Boys Girls } \\
& \left. \begin{array} { r r r r r r r r | r r r r r r r r r r r r r }
& 677664 & 4 & 3 & 0 & 0 & 5 & 5 & 6 & 677888
\end{array} \right\}
\end{aligned}$$
Key: 4 | 2 | 2 means a boy who watched 24 hours and a girl who watched 22 hours of television per week.\\
(i) Find the median and the quartiles of the results for the boys.\\
(ii) Give a reason why the median might be preferred to the mean in using an average to compare the two data sets.\\
(iii) State one advantage, and one disadvantage, of using stem-and-leaf diagrams rather than box-andwhisker plots to represent the data.
\hfill \mbox{\textit{OCR S1 2005 Q2 [6]}}