# Exam-Style Question on Correlation

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 98. This question is similar to one that appeared on an IB Studies paper in 2014. The use of a calculator is allowed.

As part of a conservation project, Darren was asked to measure the circumference of trees that were growing at different distances from a beach.

His results are shown in the following table.

 Distance, $$x$$ (metres) 6 14 20 25 35 48 46 48 52 Circumference, $$y$$ (centimetres) 52 57 57 68 65 70 75 80 82

(a) State whether distance from the beach is a continuous or discrete variable.

(b) On graph paper, draw a scatter diagram to show Darren’s results. Use a scale of 1 cm to represent 5 m on the x-axis and 1 cm to represent 10 cm on the y-axis.

(c) Calculate the mean distance, $$\bar x$$ , of the trees from the beach.

(d) Work out the mean circumference, $$\bar y$$ , of the trees.

(e) Plot and label the point M($$\bar x,\bar y$$) on your graph.

(f) Write down the Pearson’s product–moment correlation coefficient, $$r$$ , for Darren's results.

(g) Find the equation of the regression line $$y$$ on $$x$$, for Darren’s results.

(h) Draw the regression line $$y$$ on $$x$$ on your graph.

(i) Use the equation of the regression line $$y$$ on $$x$$ to estimate the circumference of a tree that is 42 m from the beach.

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