Moderate -0.5 This is a straightforward calculation of the product-moment correlation coefficient from raw bivariate data using the standard formula. While it involves multiple arithmetic steps and careful organization of calculations (Σx, Σy, Σx², Σy², Σxy), it requires only direct application of a memorized formula with no conceptual insight or problem-solving. The computational burden makes it slightly easier than average since it's purely mechanical.
3 Fourteen candidates each sat two test papers, Paper 1 and Paper 2, on the same day. The marks, out of a total of 50, achieved by the students on each paper are shown in the table.
Group T (\(r = 0.261\)): weak positive correlation between Paper 1 and Paper 2 marks
B1
In context
Group U (\(r \approx 0.615\)): moderate positive correlation between Paper 1 and Paper 2 marks
B1
In context
Part (b)(iii)
Answer
Marks
Guidance
Answer
Mark
Guidance
Extra tuition appears to have improved marks (Group T has higher means: \(\bar{x}=33.57\), \(\bar{y}=39.86\) vs Group U \(\bar{x}=18.43\), \(\bar{y}=18.14\))
B1
Comparison of means with values
But lower correlation for Group T suggests extra tuition benefited some more than others / relationship less consistent
B1
Must be justified with reference to \(r\) values
# Question 3:
## Part (a)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $S_{xx}$, $S_{yy}$, $S_{xy}$ calculated from all 14 candidates | M1 | Correct formula attempted |
| $r = \frac{S_{xy}}{\sqrt{S_{xx} \cdot S_{yy}}}$ | M1 | Correct structure |
| $r = \mathbf{0.970}$ (or equivalent) | A1 | awrt 0.970 |
## Part (a)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Strong positive (linear) correlation between marks on Paper 1 and Paper 2 | B1 | Must reference context |
| Candidates who scored highly on Paper 1 tended to score highly on Paper 2 | B1 | |
## Part (b)(i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $r = \frac{S_{xy}}{\sqrt{S_{xx} \cdot S_{yy}}} = \frac{34.57}{\sqrt{279.71 \times 112.86}}$ | M1 | Correct substitution |
| $r = \mathbf{0.615}$ | A1 | awrt 0.615 |
## Part (b)(ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Group T ($r = 0.261$): weak positive correlation between Paper 1 and Paper 2 marks | B1 | In context |
| Group U ($r \approx 0.615$): moderate positive correlation between Paper 1 and Paper 2 marks | B1 | In context |
## Part (b)(iii)
| Answer | Mark | Guidance |
|--------|------|----------|
| Extra tuition appears to have improved marks (Group T has higher means: $\bar{x}=33.57$, $\bar{y}=39.86$ vs Group U $\bar{x}=18.43$, $\bar{y}=18.14$) | B1 | Comparison of means with values |
| But lower correlation for Group T suggests extra tuition benefited some more than others / relationship less consistent | B1 | Must be justified with reference to $r$ values |
3 Fourteen candidates each sat two test papers, Paper 1 and Paper 2, on the same day. The marks, out of a total of 50, achieved by the students on each paper are shown in the table.
\hfill \mbox{\textit{AQA S1 2015 Q3 [11]}}