| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Assess appropriateness of correlation analysis |
| Difficulty | Moderate -0.5 This is a data handling question requiring interpretation of correlation and basic linear regression application. Parts (a)-(d) test understanding of data quality and correlation concepts at a basic level. Part (e) requires recognizing that high correlation suggests linear relationship (standard textbook reasoning). Part (f) is straightforward substitution into a given linear model. While multi-part, each component is routine for Further Maths Statistics with no novel problem-solving required. |
| Spec | 2.02j Clean data: missing data, errors |
| A | B | C | D | E | F | G | H | |
| 1 | Sex | Age | Marital | Weight | Height | BMI | Waist | Pulse |
| 2 | Female | 34 | Married | 60.3 | 173.4 | 20.05 | 82.5 | 74 |
| 3 | Female | 85 | Widowed | 64.7 | 161.2 | 24.9 | \#N/A | \#N/A |
| 4 | Female | 48 | Divorced | 100.6 | 171.4 | 34.24 | 105.6 | 92 |
| 5 | Male | 61 | Married | 70.9 | 169.5 | 24.68 | 92.2 | 70 |
| 6 | Male | 68 | Divorced | 96.8 | 181.6 | 29.35 | 112.9 | 68 |
| Answer | Marks | Guidance |
|---|---|---|
| \#N/A is used to stop the software reading the entry as zero | B1 | AO2.4 |
| Answer | Marks | Guidance |
|---|---|---|
| \((30.6, 128)\) and \((1.3, 88)\) ringed | B1 | AO1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| Outlier on extreme left should be removed as nobody could have a BMI this low | B1 | AO2.4 |
| Outlier with (very) high pulse rate should not be removed as it is plausible | B1 | AO2.4 |
| Answer | Marks | Guidance |
|---|---|---|
| No correlation | B1 | AO2.2b |
| Answer | Marks | Guidance |
|---|---|---|
| Because the value of pmcc is close to 1 or because there is strong correlation | B1 | AO2.2b |
| Answer | Marks | Guidance |
|---|---|---|
| \(86.784\), \(86.78\) or \(86.8\) | B1 | AO3.4 |
# Question 12:
## Part (a):
\#N/A is used to stop the software reading the entry as zero | **B1** | AO2.4 | Allow so that the cell is ignored or the software interprets \#N/A as no data
**[1 mark]**
## Part (b):
$(30.6, 128)$ and $(1.3, 88)$ ringed | **B1** | AO1.1 |
**[1 mark]**
## Part (c):
Outlier on extreme left should be removed as nobody could have a BMI this low | **B1** | AO2.4 | Need to refer to BMI being implausible
Outlier with (very) high pulse rate should not be removed as it is plausible | **B1** | AO2.4 |
**[2 marks]**
## Part (d):
No correlation | **B1** | AO2.2b | Ignore other comments unless contradictory
**[1 mark]**
## Part (e):
Because the value of pmcc is close to 1 or because there is strong correlation | **B1** | AO2.2b |
**[1 mark]**
## Part (f):
$86.784$, $86.78$ or $86.8$ | **B1** | AO3.4 | isw
**[1 mark]**
---12 Fig. 12.1 shows an excerpt from the pre-release material.
\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
& A & B & C & D & E & F & G & H \\
\hline
1 & Sex & Age & Marital & Weight & Height & BMI & Waist & Pulse \\
\hline
2 & Female & 34 & Married & 60.3 & 173.4 & 20.05 & 82.5 & 74 \\
\hline
3 & Female & 85 & Widowed & 64.7 & 161.2 & 24.9 & \#N/A & \#N/A \\
\hline
4 & Female & 48 & Divorced & 100.6 & 171.4 & 34.24 & 105.6 & 92 \\
\hline
5 & Male & 61 & Married & 70.9 & 169.5 & 24.68 & 92.2 & 70 \\
\hline
6 & Male & 68 & Divorced & 96.8 & 181.6 & 29.35 & 112.9 & 68 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 12.1}
\end{center}
\end{table}
There was no data available for cell H3.
\begin{enumerate}[label=(\alph*)]
\item Explain why \#N/A is used when no data is available.
Fig. 12.2 shows a scatter diagram of pulse rate against BMI (Body Mass Index) for females. All the available data was used.
Pulse rate against BMI for females
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c9d14a4d-a1c8-42ad-9c0b-42cef6b3612f-08_659_1552_1363_233}
\captionsetup{labelformat=empty}
\caption{Fig. 12.2}
\end{center}
\end{figure}
There are two outliers on the diagram.
\item On the copy of Fig. 12.2 in the Printed Answer Booklet, ring these outliers.
\item Use your knowledge of the pre-release material to explain whether either of these outliers should be removed.
\item State whether the diagram suggests there is any correlation between pulse rate and BMI.
The product moment correlation coefficient between waist measurement, $w$, in cm and BMI, $b$, for females was found to be 0.912 . All the available data was used.
\item Explain why a model of the form $\mathrm { w } = \mathrm { mb } + \mathrm { c }$ for the relationship between waist measurement and BMI is likely to be appropriate.
The LINEST function on a spreadsheet gives $m = 2.16$ and $c = 33.0$.
\item Calculate an estimate of the value for cell G3 in Fig. 12.1.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2021 Q12 [5]}}