AQA S1 2011 January — Question 1

Exam BoardAQA
ModuleS1 (Statistics 1)
Year2011
SessionJanuary
TopicBivariate data
TypeEstimate correlation from scatter diagram
1
  1. Estimate, without undertaking any calculations, the value of the product moment correlation coefficient between the variables \(x\) and \(y\) for each of the two scatter diagrams. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{(i)} \includegraphics[alt={},max width=\textwidth]{156f9453-ebc6-4406-b5bc-08d1918ebc62-02_487_652_733_356}
    \end{figure} \includegraphics[max width=\textwidth, alt={}, center]{156f9453-ebc6-4406-b5bc-08d1918ebc62-02_576_714_733_1153}
  2. The table gives the circumference, \(x\) centimetres, and the weight, \(y\) grams, of each of 12 new cricket balls.
    \(\boldsymbol { x }\)22.522.722.622.422.522.822.622.722.822.422.922.6
    \(\boldsymbol { y }\)160.3159.4157.8158.0157.3159.8158.3159.6161.3156.4162.5161.2
    1. Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
    2. Assuming that the 12 balls may be considered to be a random sample, interpret your value in context.
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