## Exam Style Question## Worked solutions to typical exam type questions that you can reveal gradually |

Question id: 98. This question is similar to one that appeared in 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.

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

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

©1997 - 2019 Transum Mathematics :: For more exam type questions and worked solutions go to Transum.org/Maths/Exam/