| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2020 |
| Session | November |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Assess appropriateness of correlation analysis |
| Difficulty | Moderate -0.8 This is a straightforward AS-level statistics question testing basic concepts: simple BMI calculation using a formula, reading correlation from a scatter diagram, interpolation/extrapolation awareness, and sampling methods. All parts require recall of standard definitions and procedures with no problem-solving or novel insight needed. Easier than average A-level content. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation5.09a Dependent/independent variables |
| Sex | Age in years | Mass in kg | Height in cm | BMI |
| Male | 38 | 77.6 | 164.8 | 28.57 |
| Male | 17 | 63.5 | 170.3 | 21.89 |
| Male | 18 | 68.0 | 172.3 | 22.91 |
| Male | 18 | 57.2 | 172.2 | 19.29 |
| Male | 19 | 77.6 | 191.2 | 21.23 |
| Male | 24 | 72.7 | 177.0 | 23.21 |
| Male | 25 | 92.5 | 177.9 | 29.23 |
| Male | 26 | 70.4 | 159.4 | 27.71 |
| Male | 31 | 77.5 | 174.0 | 25.60 |
| Male | 34 | 132.4 | 182.2 | 39.88 |
| Male | 38 | 115.0 | 186.4 | 33.10 |
| Male | 40 | 112.1 | 171.7 | 38.02 |
| Answer | Marks | Guidance |
|---|---|---|
| Mass \(= 23.56 \times 1.816^2\) | M1 (1.1) | Allow M1 for cm used here |
| \(= 77.7\) [kg] | A1 (1.1) [2] | CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Positive [correlation] | B1 (1.1) [1] | Ignore e.g. weak or strong; accept 'as age increases so does BMI' oe |
| Answer | Marks |
|---|---|
| \(28 \leq \text{BMI} < 30\) | B1 (3.4) [1] |
| Answer | Marks | Guidance |
|---|---|---|
| extrapolation | B1 (3.5b) [1] | Or equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| e.g. females in population | B1 (2.2b) | any two distinct comments |
| wider age range in population | B1 (2.2b) [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Generate a random number \(n\) between 1 and (e.g. 20) inclusive and select the \(n\)th item in the data set OR select every \(m\)th (e.g. 16th value) | M1 (1.2) | Random no between 1 and 9 and every 17th item would also work; random no between 1 and 31, and then every 15th item also works, etc. |
| For valid solution | A1 (1.1) [2] |
## Question 10(a):
Mass $= 23.56 \times 1.816^2$ | M1 (1.1) | Allow M1 for cm used here
$= 77.7$ [kg] | A1 (1.1) **[2]** | CAO
---
## Question 10(b):
Positive [correlation] | B1 (1.1) **[1]** | Ignore e.g. weak or strong; accept 'as age increases so does BMI' oe
---
## Question 10(c):
$28 \leq \text{BMI} < 30$ | B1 (3.4) **[1]** |
---
## Question 10(d):
extrapolation | B1 (3.5b) **[1]** | Or equivalent
---
## Question 10(e):
e.g. females in population | B1 (2.2b) | any two distinct comments
wider age range in population | B1 (2.2b) **[2]** |
scatter diagram for whole population shows very weak negative correlation
---
## Question 10(f):
Generate a random number $n$ between 1 and (e.g. 20) inclusive and select the $n$th item in the data set OR select every $m$th (e.g. 16th value) | M1 (1.2) | Random no between 1 and 9 and every 17th item would also work; random no between 1 and 31, and then every 15th item also works, etc.
For valid solution | A1 (1.1) **[2]** |
---10 Fig. 10.1 shows a sample collected from the large data set.
BMI is defined as $\frac { \text { mass of person in kilograms } } { \text { square of person's height in metres } }$.
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Sex & Age in years & Mass in kg & Height in cm & BMI \\
\hline
Male & 38 & 77.6 & 164.8 & 28.57 \\
\hline
Male & 17 & 63.5 & 170.3 & 21.89 \\
\hline
Male & 18 & 68.0 & 172.3 & 22.91 \\
\hline
Male & 18 & 57.2 & 172.2 & 19.29 \\
\hline
Male & 19 & 77.6 & 191.2 & 21.23 \\
\hline
Male & 24 & 72.7 & 177.0 & 23.21 \\
\hline
Male & 25 & 92.5 & 177.9 & 29.23 \\
\hline
Male & 26 & 70.4 & 159.4 & 27.71 \\
\hline
Male & 31 & 77.5 & 174.0 & 25.60 \\
\hline
Male & 34 & 132.4 & 182.2 & 39.88 \\
\hline
Male & 38 & 115.0 & 186.4 & 33.10 \\
\hline
Male & 40 & 112.1 & 171.7 & 38.02 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 10.1}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Calculate the mass in kg of a person with a BMI of 23.56 and a height of 181.6 cm , giving your answer correct to 1 decimal place.
Fig. 10.2 shows a scatter diagram of BMI against age for the data in the table. A line of best fit has also been drawn.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c08a2212-3104-425e-8aee-7f2d46f23924-09_682_1212_351_248}
\captionsetup{labelformat=empty}
\caption{Fig. 10.2}
\end{center}
\end{figure}
\item Describe the correlation between age and BMI.
\item Use the line of best fit to estimate the BMI of a 30-year-old man.
\item Explain why it would not be sensible to use the line of best fit to estimate the BMI of a 60-year-old man.
\item Use your knowledge of the large data set to suggest two reasons why the sample data in the table may not be representative of the population.
\item Once the data in the large data set had been cleaned there were 196 values available for selection. Describe how a sample of size 12 could be generated using systematic sampling so that each of the 196 values could be selected in the sample.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2020 Q10 [9]}}