| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Critique given sampling method |
| Difficulty | Easy -1.2 This question tests basic understanding of sampling methods and reading cumulative frequency curves. Part (a) requires simple recall of random sampling definition, part (b) involves straightforward reading of values from a graph, and part (c) asks for elementary reasoning about sample variability. All parts are conceptual with minimal calculation, well below average A-level difficulty. |
| Spec | 2.01c Sampling techniques: simple random, opportunity, etc2.01d Select/critique sampling: in context2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| not a simple random sample since each possible sample does not have an equal probability of being selected | B1 (2.4) | allow "not a simple random sample since each plant does not have an equal probability of being selected"; ignore further comments unless contradictory; the essential elements of the comment are in bold |
| Answer | Marks | Guidance |
|---|---|---|
| \(18\) (shorter than 40 cm) seen | B1 (2.1) | may be embedded in calculation |
| \(110\) (shorter than 80 cm) or \(10\) (taller than 80 cm) seen | B1 (1.1) | may be embedded in calculation |
| \(\frac{92}{120}\) oe or \(\frac{28}{120}\) oe | M1 (1.1) | FT their 18 and their 110; allow M1 for \(\frac{91}{120}\) or \(\frac{29}{120}\) oe; or \(\frac{75}{100} \times 120 = 90\) oe |
| awrt \(77\% > 75\%\) oe so this supports the (owner's) statement | A1 (2.2a) | or \(92 > 90\) so this supports the (owner's) statement; need comparison and comment |
| Answer | Marks | Guidance |
|---|---|---|
| must refer to sample in answer; eg since different samples give different results, not all samples would necessarily support owner's statement; eg no since another sample may contain all the tallest plants (and/or shortest); eg no since the heights in other samples may be different | B1 (2.4) | ignore superfluous comments referring to eg growing conditions, soil type etc; do not allow: eg no, conditions different for other plants; eg no, different plants on different rows; eg no, might be biggest and smallest plants on other rows; eg the first sample is not representative |
## Question 8(a):
not a simple random sample since each possible sample does not have an equal probability of being selected | B1 (2.4) | allow "not a simple random sample since each plant does not have an equal probability of being selected"; ignore further comments unless contradictory; the essential elements of the comment are in bold
## Question 8(b):
$18$ (shorter than 40 cm) seen | B1 (2.1) | may be embedded in calculation
$110$ (shorter than 80 cm) or $10$ (taller than 80 cm) seen | B1 (1.1) | may be embedded in calculation
$\frac{92}{120}$ oe or $\frac{28}{120}$ oe | M1 (1.1) | FT their 18 and their 110; allow M1 for $\frac{91}{120}$ or $\frac{29}{120}$ oe; or $\frac{75}{100} \times 120 = 90$ oe
awrt $77\% > 75\%$ oe so this supports the (owner's) statement | A1 (2.2a) | or $92 > 90$ so this supports the (owner's) statement; need comparison and comment
## Question 8(c):
must refer to sample in answer; eg since different samples give different results, not all samples would necessarily support owner's statement; eg no since another sample may contain all the tallest plants (and/or shortest); eg no since the heights in other samples may be different | B1 (2.4) | ignore superfluous comments referring to eg growing conditions, soil type etc; do not allow: eg no, conditions different for other plants; eg no, different plants on different rows; eg no, might be biggest and smallest plants on other rows; eg the first sample is not representative8 A garden centre stocks coniferous hedging plants. These are displayed in 10 rows, each of 120 plants. An employee collects a sample of the heights of these plants by recording the height of each plant on the front row of the display.
\begin{enumerate}[label=(\alph*)]
\item Explain whether the data collected by the employee is a simple random sample.
The data are shown in the cumulative frequency curve below.\\
\includegraphics[max width=\textwidth, alt={}, center]{11788aaf-98fb-4a78-8a40-a40743b1fe15-06_1376_1344_680_233}
The owner states that at least $75 \%$ of the plants are between 40 cm and 80 cm tall.
\item Show that the data collected by the employee supports this statement.
\item Explain whether all samples of 120 plants would necessarily support the owner's statement.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2023 Q8 [6]}}