| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate summary statistics (Sxx, Syy, Sxy) |
| Difficulty | Easy -1.2 This is a straightforward application of standard formulas for Sxx, Sxy, and correlation coefficient with all necessary summations provided. Parts (a) and (b) require only direct substitution into memorized formulas, while part (c) tests basic understanding of correlation transitivity. No problem-solving or novel insight required—purely routine calculation and recall. |
| Spec | 2.02c Scatter diagrams and regression lines2.02d Informal interpretation of correlation5.09a Dependent/independent variables |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((S_{tt}) = 8702 - \frac{258^2}{10}\) or \((S_{gt}) = 1550.2 - \frac{258 \times 63.6}{10}\) | M1 | For at least one correct expression |
| \((S_{tt} =) 2045.6\), \((S_{gt} =) -90.68\) | A1, A1 | 1st A1: \(S_{tt}\) = awrt 2046 (condone \(S_{xx} = \ldots\) or \(S_{yy} = \ldots\)); 2nd A1: \(S_{gt}\) = awrt \(-90.7\) (condone \(S_{xy} = \ldots\)) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(r = \frac{-90.68}{\sqrt{2045.6 \times 7.864}} = -0.714956\ldots\) awrt \(-0.715\) | M1 A1 | M1 for attempt at correct formula; must have \(S_{tt}\), \(S_{gt}\) and \(S_{gg}\) in correct places; condone missing "\(-\)"; Award M1A0 for awrt \(-0.71\) with no expression seen; M0 for \(\frac{1550.2}{\sqrt{8702 \times 7.864}}\); correct answer only is 2/2 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Positive | B1 | 1st B1 for saying "positive"; ignore mention of skew |
| e.g. high \(v\) corresponds to low \(t\) and low \(t\) corresponds to high \(g\) so expect high \(v\) to correspond to high \(g\); or expect more revision to result in a better grade | B1 | 2nd B1 for suitable reason mentioning at least \(v\) and \(g\) supporting positive correlation; "the less revision done the lower the grade" is B1; "should do better with more revision" is B0 since does not mention grades; "both coefficients are similar" or two sketches of negative correlation with labelled axes is B1 since \(v\), \(t\) and \(g\) are implied; allow use of letters \(v\) and \(g\); allow equivalent terms e.g. "study" instead of "revision" or "score" instead of "grade" |
## Question 1:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(S_{tt}) = 8702 - \frac{258^2}{10}$ or $(S_{gt}) = 1550.2 - \frac{258 \times 63.6}{10}$ | M1 | For at least one correct expression |
| $(S_{tt} =) 2045.6$, $(S_{gt} =) -90.68$ | A1, A1 | 1st A1: $S_{tt}$ = awrt 2046 (condone $S_{xx} = \ldots$ or $S_{yy} = \ldots$); 2nd A1: $S_{gt}$ = awrt $-90.7$ (condone $S_{xy} = \ldots$) |
**Total: 3 marks**
---
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $r = \frac{-90.68}{\sqrt{2045.6 \times 7.864}} = -0.714956\ldots$ awrt $-0.715$ | M1 A1 | M1 for attempt at correct formula; must have $S_{tt}$, $S_{gt}$ and $S_{gg}$ in correct places; condone missing "$-$"; Award M1A0 for awrt $-0.71$ with no expression seen; M0 for $\frac{1550.2}{\sqrt{8702 \times 7.864}}$; correct answer only is 2/2 |
**Total: 2 marks**
---
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Positive | B1 | 1st B1 for saying "positive"; ignore mention of skew |
| e.g. high $v$ corresponds to low $t$ and low $t$ corresponds to high $g$ so expect high $v$ to correspond to high $g$; or expect more revision to result in a better grade | B1 | 2nd B1 for suitable reason mentioning at least $v$ and $g$ supporting positive correlation; "the less revision done the lower the grade" is B1; "should do better with more revision" is B0 since does not mention grades; "both coefficients are similar" or two sketches of negative correlation with labelled axes is B1 since $v$, $t$ and $g$ are implied; allow use of letters $v$ and $g$; allow equivalent terms e.g. "study" instead of "revision" or "score" instead of "grade" |
**Total: 2 marks**
**Question 1 Total: 7 marks**\begin{enumerate}
\item A teacher asked a random sample of 10 students to record the number of hours of television, $t$, they watched in the week before their mock exam. She then calculated their grade, $g$, in their mock exam. The results are summarised as follows.
\end{enumerate}
$$\sum t = 258 \quad \sum t ^ { 2 } = 8702 \quad \sum g = 63.6 \quad \mathrm {~S} _ { g g } = 7.864 \quad \sum g t = 1550.2$$
(a) Find $\mathrm { S } _ { t t }$ and $\mathrm { S } _ { g t }$\\
(b) Calculate, to 3 significant figures, the product moment correlation coefficient between $t$ and $g$.
The teacher also recorded the number of hours of revision, $v$, these 10 students completed during the week before their mock exam. The correlation coefficient between $t$ and $v$ was -0.753\\
(c) Describe, giving a reason, the nature of the correlation you would expect to find between $v$ and $g$.\\
\hfill \mbox{\textit{Edexcel S1 2013 Q1 [7]}}