| Exam Board | OCR |
|---|---|
| Module | Further Statistics AS (Further Statistics AS) |
| Year | 2020 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from raw bivariate data |
| Difficulty | Moderate -0.3 This is a straightforward calculation of Pearson's correlation coefficient from a small dataset (5 points), followed by interpretation and understanding of linear transformations. Part (a) is routine computation using the standard formula, part (b) tests basic interpretation, and part (c) tests understanding that linear transformations preserve correlation. While it requires careful arithmetic and knowledge of correlation properties, it's a standard textbook exercise with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.08a Pearson correlation: calculate pmcc |
| \(x\) | 7 | 8 | 12 | 6 | 4 |
| \(y\) | 20 | 16 | 7 | 17 | 23 |
| Answer | Marks | Guidance |
|---|---|---|
| \(-0.954\) | B2 [2] | SC: If B0, give B1 if two of \(7.04, 29.0[4], -13.6[4]\) (or \(35.2, 145[.2], -68.2\)) seen |
| Answer | Marks | Guidance |
|---|---|---|
| Points lie close to a straight line | B1 | Must refer to line, not just "negative correlation" |
| Line has negative gradient | B1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| No, it will be the same as \(x \to a\) is a linear transformation | B1 [1] | OE. *Either* "same" with correct reason, *or* "disagree" with correct reason. Allow any clear valid technical term |
# Question 1:
## Part (a)
$-0.954$ | **B2** [2] | SC: If B0, give B1 if two of $7.04, 29.0[4], -13.6[4]$ (or $35.2, 145[.2], -68.2$) seen
## Part (b)
Points lie close to a straight line | **B1** | Must refer to line, not just "negative correlation"
Line has negative gradient | **B1** [2] |
## Part (c)
No, it will be the same as $x \to a$ is a linear transformation | **B1** [1] | OE. *Either* "same" with correct reason, *or* "disagree" with correct reason. Allow any clear valid technical term
---1 Five observations of bivariate data $( x , y )$ are given in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
$x$ & 7 & 8 & 12 & 6 & 4 \\
\hline
$y$ & 20 & 16 & 7 & 17 & 23 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find the value of Pearson's product-moment correlation coefficient.
\item State what your answer to part (a) tells you about a scatter diagram representing the data.
\item A new variable $a$ is defined by $\mathrm { a } = 3 \mathrm { x } + 4$. Dee says "The value of Pearson's product-moment correlation coefficient between $a$ and $y$ will not be the same as the answer to part (a)."
State with a reason whether you agree with Dee.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics AS 2020 Q1 [5]}}