| Exam Board | OCR |
|---|---|
| Module | FS1 AS (Further Statistics 1 AS) |
| Year | 2018 |
| Session | March |
| Marks | 4 |
| Topic | Bivariate data |
| Type | Distinguish dependent and independent variables |
| Difficulty | Easy -1.8 This question tests basic conceptual understanding of correlation coefficients with minimal calculation. Parts (i)-(iii) require only recall of definitions: controlled variables, invariance of r under linear transformations, and that r_s equals r when data is monotonic. Part (iv) needs recognition that r measures linear strength while r_s measures monotonic relationships. No problem-solving or multi-step reasoning required. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08e Spearman rank correlation5.08g Compare: Pearson vs Spearman |
| Answer | Marks | Guidance |
|---|---|---|
| \(t\) is a controlled variable | B1 | 2.5 |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.987\) | B1 | 1.2 |
| Answer | Marks | Guidance |
|---|---|---|
| \(1\) | B1 | 2.2a |
| Answer | Marks | Guidance |
|---|---|---|
| Points lie close to a straight line | B1 | 2.2b |
### Part (i)
$t$ is a controlled variable | **B1** | 2.5
### Part (ii)
$0.987$ | **B1** | 1.2 | Or "unchanged"
### Part (iii)
$1$ | **B1** | 2.2a
### Part (iv)
Points lie close to a straight line | **B1** | 2.2b | Not "positive gradient" – that information is given by $r$
---5 The speed $v \mathrm {~ms} ^ { - 1 }$ of a car at time $t$ seconds after it starts to accelerate was measured at 1 -second intervals. The results are shown in the following diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{d5843350-52f9-4fed-adf4-86ceb958033f-3_661_1186_1078_443}\\
(i) State whether $t$ or $v$ or neither is a controlled variable.
The value of the product moment correlation coefficient $r$ for the data is 0.987 correct to 3 significant figures.\\
(ii) The speed of the car is converted to miles per hour and the time to minutes. State the value of $r$ for the converted data.\\
(iii) State the value of Spearman's rank correlation coefficient $r _ { s }$ for the data.\\
(iv) What information does $r$ give about the data that is not given by $r _ { s }$ ?
\hfill \mbox{\textit{OCR FS1 AS 2018 Q5 [4]}}