| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2020 |
| Session | November |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Estimate mean and standard deviation from frequency table |
| Difficulty | Moderate -0.8 This is a straightforward AS-level statistics question requiring basic understanding of cumulative frequency diagrams. Part (a) involves checking which diagram matches the given frequency table (simple arithmetic verification), and part (b) requires reading the median from a cumulative frequency curve at the 48.5th position—both are standard textbook exercises with no problem-solving or novel insight required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Arm length in cm | \(30 -\) | \(31 -\) | \(32 -\) | \(33 -\) | \(34 -\) | \(35 -\) | \(36 -\) | \(37 -\) | \(38 -\) | \(39 -\) | \(40 - 41\) |
| Frequency | 1 | 4 | 5 | 9 | 13 | 19 | 17 | 17 | 4 | 3 | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Diagram A is incorrect | B1 (2.2a) | Accept diagram B is correct |
| The cumulative frequencies have been plotted at the left hand end of each class interval, not at the right hand end | B1 (2.3) | Oe, e.g. Used lower bound not upper bound |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| 35.7 to 35.9 inclusive | B1 (1.1) | From diagram, but ignore any calculation; allow even if wrong diagram given in (a). If they say Diagram B is incorrect oe in (a), allow sc B1 for 34.7 to 34.9 inclusive |
| [1] |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Diagram A is incorrect | B1 (2.2a) | Accept diagram B is correct |
| The cumulative frequencies have been plotted at the left hand end of each class interval, not at the right hand end | B1 (2.3) | Oe, e.g. Used lower bound not upper bound |
| **[2]** | | |
---
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| 35.7 to 35.9 inclusive | B1 (1.1) | From diagram, but ignore any calculation; allow even if wrong diagram given in (a). If they say Diagram B is incorrect oe in (a), allow sc B1 for 34.7 to 34.9 inclusive |
| **[1]** | | |
---2 A student measures the upper arm lengths of a sample of 97 women. The results are summarised in the frequency table in Fig. 2.1.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | c | }
\hline
Arm length in cm & $30 -$ & $31 -$ & $32 -$ & $33 -$ & $34 -$ & $35 -$ & $36 -$ & $37 -$ & $38 -$ & $39 -$ & $40 - 41$ \\
\hline
Frequency & 1 & 4 & 5 & 9 & 13 & 19 & 17 & 17 & 4 & 3 & 5 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 2.1}
\end{center}
\end{table}
The student constructs two cumulative frequency diagrams to represent the data using different class intervals. These are shown in Fig. 2.2 opposite
One of these diagrams is correct and the other is incorrect.
\begin{enumerate}[label=(\alph*)]
\item State which diagram is incorrect, justifying your answer.
\item Use the correct diagram in Fig. 2.2 to find an estimate of the median.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c08a2212-3104-425e-8aee-7f2d46f23924-05_2256_1230_191_148}
\captionsetup{labelformat=empty}
\caption{Fig. 2.2}
\end{center}
\end{figure}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2020 Q2 [3]}}