| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear regression |
| Type | Interpret regression line parameters |
| Difficulty | Easy -1.8 This is a statistics question testing basic data interpretation and sampling concepts at AS level. It requires identifying graph errors, reading values from a line of best fit, understanding extrapolation limitations, and describing systematic sampling—all routine recall and application with no mathematical calculation complexity or novel problem-solving required. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation2.02i Select/critique data presentation |
| Answer | Marks | Guidance |
|---|---|---|
| 11 | (i) | Any two distinct reasons |
| Answer | Marks |
|---|---|
| gaps between bars | E1 |
| Answer | Marks |
|---|---|
| [2] | 2.4 |
| Answer | Marks | Guidance |
|---|---|---|
| 11 | (ii) | A |
| [1] | 2.2b | oe |
| 11 | (ii) | B |
| [1] | 1.1 | |
| 11 | (ii) | C |
| [1] | 3.2b | oe |
| 11 | (ii) | D |
| may be very different from those in Africa. | E1 | |
| [1] | 2.2a | oe |
| 11 | (ii) | E |
| [1] | 2.2a | eg a random sample would almost |
| Answer | Marks | Guidance |
|---|---|---|
| from Africa | Advantage | |
| 11 | (iii) | Eg Generate a random number, n, between 1 and |
| Answer | Marks |
|---|---|
| (stopping when 14 have been selected) | B1 |
| Answer | Marks |
|---|---|
| [2] | 1.2 |
| 1.1 | Candidates may choose other valid |
Question 11:
11 | (i) | Any two distinct reasons
eg classes of different widths represented by bars
of same width
eg vertical axis should be frequency density
eg final upper class boundary not given
eg should have continuous horizontal scale / no
gaps between bars | E1
E1
[2] | 2.4
1.1
11 | (ii) | A | Positive correlation | B1
[1] | 2.2b | oe
11 | (ii) | B | 9.8395 or 9.8 or 9.84 or 9.840 | B1
[1] | 1.1
11 | (ii) | C | extrapolation | B1
[1] | 3.2b | oe
11 | (ii) | D | Birth rates and death rates in the Caribbean,
may be very different from those in Africa. | E1
[1] | 2.2a | oe | Advantage
11 | (ii) | E | eg other continents to select countries from | E1
[1] | 2.2a | eg a random sample would almost
certainly not just include countries
from Africa | Advantage
11 | (iii) | Eg Generate a random number, n, between 1 and
4 and select the nth item in the data set.
Eg Select every 4th item on the list thereafter
(stopping when 14 have been selected) | B1
B1
[2] | 1.2
1.1 | Candidates may choose other valid
starting points
Candidates may choose other valid
intervalsThe pre-release material contains data concerning the death rate per thousand people and the birth rate per thousand people in all the countries of the world. The diagram in Fig. 11.1 was generated using a spreadsheet and summarises the birth rates for all the countries in Africa.
\includegraphics{figure_11_1}
Fig. 11.1
\begin{enumerate}[label=(\roman*)]
\item Identify two respects in which the presentation of the data is incorrect. [2]
\end{enumerate}
Fig. 11.2 shows a scatter diagram of death rate, $y$, against birth rate, $x$, for a sample of 55 countries, all of which are in Africa. A line of best fit has also been drawn.
\includegraphics{figure_11_2}
Fig. 11.2
The equation of the line of best fit is $y = 0.15x + 4.72$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item \begin{enumerate}[label=(\Alph*)]
\item What does the diagram suggest about the relationship between death rate and birth rate? [1]
\item The birth rate in Togo is recorded as 34.13 per thousand, but the data on death rate has been lost. Use the equation of the line of best fit to estimate the death rate in Togo. [1]
\item Explain why it would not be sensible to use the equation of the line of best fit to estimate the death rate in a country where the birth rate is 5.5 per thousand. [1]
\item Explain why it would not be sensible to use the equation of the line of best fit to estimate the death rate in a Caribbean country where the birth rate is known. [1]
\item Explain why it is unlikely that the sample is random. [1]
\end{enumerate}
\end{enumerate}
Including Togo there were 56 items available for selection.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Describe how a sample of size 14 from this data could be generated for further analysis using systematic sampling. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2018 Q11 [9]}}