| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Compare or interpret cumulative frequency graphs |
| Difficulty | Moderate -0.5 This is a straightforward cumulative frequency interpretation question requiring reading values from graphs (median at n/2), comparing distributions using median/quartiles, and finding corresponding percentiles. While multi-part, each component uses standard S1 techniques with no complex reasoning or calculation required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| \(m_1 = 38, m_2 = 63\) | M1 | For reading off at 1000; may be implied |
| A1 | For correct value for either median | |
| A1 | For both correct |
| Answer | Marks | Guidance |
|---|---|---|
| Marks were higher on paper 2 | B1 | For a correct statement |
| B1 | For a correct justification |
| Answer | Marks | Guidance |
|---|---|---|
| Proportion is \(\frac{2000 - 1700}{2000}\), i.e. 15% | M1 | For reading off at 66; may be implied |
| A1 | For stating the correct mark | |
| M1 | For relevant subtraction from 2000 | |
| A1 | For correct answer 15% or equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| etc | B1 | For any one valid comment |
| B1 | For any other valid comment |
**Part (i)**
Medians correspond to 1000 candidates
$m_1 = 38, m_2 = 63$ | M1 | For reading off at 1000; may be implied
| A1 | For correct value for either median
| A1 | For both correct
**Part (ii)**
Paper 2 was easier
Marks were higher on paper 2 | B1 | For a correct statement
| B1 | For a correct justification
**Part (iii)**
66 marks on paper 1 corresponds to 1700 cands, 1700 cands on paper 2 corresponds to 82 marks
Proportion is $\frac{2000 - 1700}{2000}$, i.e. 15% | M1 | For reading off at 66; may be implied
| A1 | For stating the correct mark
| M1 | For relevant subtraction from 2000
| A1 | For correct answer 15% or equivalent
**Part (iv)**
Possible valid comments include:
Box plots give quick direct comparisons of medians and IQRs
Box plots don't include all the information that CF graphs do
CF graphs can be used to read off values both ways round
etc | B1 | For any one valid comment
| B1 | For any other valid comment
---6\\
\includegraphics[max width=\textwidth, alt={}, center]{2fb25fc5-0445-44fa-a23e-647d14b1a376-3_803_1180_1018_413}
The diagram shows the cumulative frequency graphs for the marks scored by the candidates in an examination. The 2000 candidates each took two papers; the upper curve shows the distribution of marks on paper 1 and the lower curve shows the distribution on paper 2. The maximum mark on each paper was 100.\\
(i) Use the diagram to estimate the median mark for each of paper 1 and paper 2.\\
(ii) State with a reason which of the two papers you think was the easier one.\\
(iii) To achieve grade A on paper 1 candidates had to score 66 marks out of 100. What mark on paper 2 gives equal proportions of candidates achieving grade A on the two papers? What is this proportion?\\
(iv) The candidates' marks for the two papers could also be illustrated by means of a pair of box-and whisker plots. Give two brief comments comparing the usefulness of cumulative frequency graphs and box-and-whisker plots for representing the data.
\hfill \mbox{\textit{OCR S1 Q6 [11]}}