Question 3 - A-Level Maths

OCR S1 2010 January — Question 3 7 marks

Exam Board	OCR
Module	S1 (Statistics 1)
Year	2010
Session	January
Marks	7
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 correlation question requiring direct application of the PMCC formula with given summary statistics (part i), basic interpretation (part ii), and recall of standard properties: correlation is unitless (part iii) and removing outliers typically strengthens correlation (part iv). All parts are routine textbook exercises with no problem-solving or novel insight required.
Spec	5.08a Pearson correlation: calculate pmcc 5.08b Linear coding: effect on pmcc

The heights, \(h\) m, and weights, \(m\) kg, of five men were measured. The results are plotted on the diagram. \includegraphics{figure_3} The results are summarised as follows. \(n = 5\) \(\Sigma h = 9.02\) \(\Sigma m = 377.7\) \(\Sigma h^2 = 16.382\) \(\Sigma m^2 = 28558.67\) \(\Sigma hm = 681.612\)

Use the summarised data to calculate the value of the product moment correlation coefficient, \(r\). [3]
Comment on your value of \(r\) in relation to the diagram. [2]
It was decided to re-calculate the value of \(r\) after converting the heights to feet and the masses to pounds. State what effect, if any, this will have on the value of \(r\). [1]
One of the men had height 1.63 m and mass 78.4 kg. The data for this man were removed and the value of \(r\) was re-calculated using the original data for the remaining four men. State in general terms what effect, if any, this will have on the value of \(r\). [1]

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The heights, $h$ m, and weights, $m$ kg, of five men were measured. The results are plotted on the diagram.

\includegraphics{figure_3}

The results are summarised as follows.

$n = 5$ $\Sigma h = 9.02$ $\Sigma m = 377.7$ $\Sigma h^2 = 16.382$ $\Sigma m^2 = 28558.67$ $\Sigma hm = 681.612$

\begin{enumerate}[label=(\roman*)]
\item Use the summarised data to calculate the value of the product moment correlation coefficient, $r$. [3]

\item Comment on your value of $r$ in relation to the diagram. [2]

\item It was decided to re-calculate the value of $r$ after converting the heights to feet and the masses to pounds. State what effect, if any, this will have on the value of $r$. [1]

\item One of the men had height 1.63 m and mass 78.4 kg. The data for this man were removed and the value of $r$ was re-calculated using the original data for the remaining four men. State in general terms what effect, if any, this will have on the value of $r$. [1]
\end{enumerate}

\hfill \mbox{\textit{OCR S1 2010 Q3 [7]}}

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