AQA S1 2010 June — Question 1 5 marks

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2010
SessionJune
Marks5
PaperDownload PDF ↗
TopicBivariate data
TypeCalculate r from raw bivariate data
DifficultyModerate -0.5 This is a standard computational question requiring calculation of the product moment correlation coefficient using the formula with given bivariate data. While tedious with 10 data points, it's a routine textbook exercise testing recall of the PMCC formula and careful arithmetic—no conceptual insight or problem-solving required beyond following the standard algorithm.
Spec5.08a Pearson correlation: calculate pmcc

1 The weight, \(x \mathrm {~kg}\), and the engine power, \(y \mathrm { bhp }\), of each car in a random sample of 10 hatchback cars are shown in the table.
\(\boldsymbol { x }\)1196106213351429101213551145141712751284
\(\boldsymbol { y }\)123881501586912094143107128
  1. Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
  2. Interpret your value in the context of the question.
    \includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-03_2484_1709_223_153}

1 The weight, $x \mathrm {~kg}$, and the engine power, $y \mathrm { bhp }$, of each car in a random sample of 10 hatchback cars are shown in the table.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | c | c | }
\hline
$\boldsymbol { x }$ & 1196 & 1062 & 1335 & 1429 & 1012 & 1355 & 1145 & 1417 & 1275 & 1284 \\
\hline
$\boldsymbol { y }$ & 123 & 88 & 150 & 158 & 69 & 120 & 94 & 143 & 107 & 128 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the value of the product moment correlation coefficient between $x$ and $y$.
\item Interpret your value in the context of the question.

\begin{center}
\includegraphics[max width=\textwidth, alt={}]{c4844a30-6a86-49e3-b6aa-8e213dfc8ca1-03_2484_1709_223_153}
\end{center}
\end{enumerate}

\hfill \mbox{\textit{AQA S1 2010 Q1 [5]}}