# 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: 23. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.

The table below shows the scores for 12 students on two Mathematic exam papers. For the first paper calculators were allowed and for the second paper they were not.

 Paper 1 ($$x$$) Paper 2 ($$y$$) 74 73 65 75 68 72 69 71 83 68 68 73 75 83 69 77 71 77 68 76 84 69 71 75

(a) Write down the mean score on Paper 1.

(b) Write down the standard deviation of the scores for Paper 1.

(c) Find the number of students that had a score of more than one standard deviation below the mean on Paper 1.

(d) Write down the correlation coefficient, $$r$$.

(e) Write down the equation of the regression line of $$y$$ on $$x$$.

Another student scored 75 on Paper 1.

(f) Calculate an estimate of his score on Paper 2

Another student scored 88 on Paper 1.

(g) Determine whether you can use the equation of the regression line to estimate his score on Paper 2. Give a reason for your answer.

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