|
|
Exam-Style Question on StatisticsA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 604. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.
Miss Chloe Sharpe (singing teacher) was teaching nine students last year. At the end of the year the students took a singing exam and their results were reported as percentages. Chloe decided to record the average number of hours per week each student reported practising in the weeks before the examination.
These results can be seen in the table below.
| Average weekly practice time (\(p\)) | 25 | 30 | 23 | 28 | 34 | 27 | 36 | 19 | 28 |
|---|---|---|---|---|---|---|---|---|---|
| Percentage score (\(s\)) | 70 | 89 | 64 | 88 | 97 | 81 | 95 | 70 | 85 |
(a) Find Pearson's product-moment correlation coefficient, \(r\), for these data.
(b) The relationship between the variables can be modelled by the regression equation \(s = ap + b\). Write down the value of \(a\) and the value of \(b\).
(c) One of these nine students was disappointed with his result and wished he had practised more. Based on the given data, determine how his score could have been expected to alter had he practised an extra four hours per week.
|
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 about these exam-style questions? 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 - 2024 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/
