| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Bivariate data |
| Type | Calculate r from summary statistics |
| Difficulty | Moderate -0.8 This is a straightforward S1 statistics question requiring standard formula application: calculating mean, variance, and correlation coefficient from given data. All formulas are directly applicable with no conceptual challenges—purely computational work with clear steps. Easier than average A-level maths due to being routine statistical calculations with no problem-solving or interpretation complexity beyond a basic comment. |
| Spec | 2.02g Calculate mean and standard deviation5.08a Pearson correlation: calculate pmcc |
| Answer | Marks |
|---|---|
| (a) \(\sum h = 9.73\) therefore \(9.73 \div 8 = 1.22\) m | M1 A1 |
| (b) \(\sum h^2 = 12.0319\) therefore \(\text{Var.} = 12.0319 \div 8 - 1.21625^2 = 0.0247\) | B1 M1 A1 |
| (c) \(S_{hh} = 0.1978\), \(S_{vv} = 410\), \(S_{hv} = 8.935\) therefore \(r = 0.992\) | M1 A1 A1 A1 |
| (d) Shows strong positive correlation | B1 |
**(a)** $\sum h = 9.73$ therefore $9.73 \div 8 = 1.22$ m | M1 A1 |
**(b)** $\sum h^2 = 12.0319$ therefore $\text{Var.} = 12.0319 \div 8 - 1.21625^2 = 0.0247$ | B1 M1 A1 |
**(c)** $S_{hh} = 0.1978$, $S_{vv} = 410$, $S_{hv} = 8.935$ therefore $r = 0.992$ | M1 A1 A1 A1 |
**(d)** Shows strong positive correlation | B1 |
**Total marks: 10**
---The heights, $h$ m, of eight children were measured, giving the following values of $h$:
1.20, 1.12, 1.43, 0.98, 1.31, 1.26, 1.02, 1.41.
\begin{enumerate}[label=(\alph*)]
\item Find the mean height of the children. [2 marks]
\item Calculate the variance of the heights. [3 marks]
\end{enumerate}
The children were also weighed. It was found that their masses, $w$ kg, were such that
$$\sum w = 324, \quad \sum w^2 = 13532, \quad \sum wh = 403.$$
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the product-moment correlation coefficient between $w$ and $h$. [4 marks]
\item Comment briefly on the value you have obtained. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q4 [10]}}