Exam-Style Question on Correlation
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 466. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.
The Farang Parkour Team hosted a Free Running event. The judges, Anan and Jason awarded 7 competitors a score out of 10. The scores are shown in the following table.
|Anan's Score (x)||7.8||9.1||8.3||6.9||7.0||8.5||9.3|
|Jason's Score (y)||7.2||9.0||8.7||7.5||6.9||8.7||8.9|
(a) Find the Pearson’s product–moment correlation coefficient, \(r\), of these scores.
(b) Using the value of \(r\), interpret the relationship between Anan’s scores and Jason’s score.
(c) Write down the equation of the regression line \(y\) on \(x\).
(d) Use your regression equation from part (c) to estimate Jason’s score to one decimal place when Anan awards a score of 5.
(e) State whether this estimate is reliable. Justify your answer.
(f) The adjudicator for the event would like to find the Spearman’s rank correlation coefficient of the scores. Copy and complete the information in the following table.
(g) Find the value of the Spearman’s rank correlation coefficient, \(r_s\).
(h) Comment on the result obtained for \(r_s\).
The adjudicator believes Jason’s score for competitor E is too high and so decreases the score from 6.9 to 6.5.
(i) Explain why the value of the Spearman’s rank correlation coefficient \(r_s\) does not change.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
©1997 - 2020 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/