Height and Speed

This is a data-handling task for learners to work on in small groups (possibly in threes?) to perform a statistical investigation based on the question: ‘Does the height of a tennis player affect the top speed of their service?’ Learners will need to decide what information is needed and how this can be obtained. It is likely to come via the internet through appropriate searches. They will then need to travel through the data-handling cycle to arrive at a conclusion and evaluation.

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Overview of task

This is a data-handling task for learners to work on in small groups (possibly in threes?) to perform a statistical investigation based on the question: ‘Does the height of a tennis player affect the top speed of their service?’ Learners will need to decide what information is needed and how this can be obtained. It is likely to come via the internet through appropriate searches. They will then need to travel through the data-handling cycle to arrive at a conclusion and evaluation.

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Strand

Statistics

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Prior knowledge

The basic concept of correlation.

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Relevance to Core Maths qualifications

  • AQA
  • C&G
  • Eduqas
  • Pearson / Edexcel
  • OCR

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Suggested approaches

This task covers these three assessment objectives:

  • Fluency: Data collection; correlation scatter graphs; lines of best fit; linear regression model (extension). Correlation coefficients and Spearman’s Rank.
  • Reasoning: Use the data analysis to reason an argument for a statement arising out of the hypothesis. Comment on the validity and accuracy of the data, including any assumptions.
  • Problem solving: Encourage the students to take the statement and decide on all the next steps.

Pose the question and in small groups facilitate a discussion about how to proceed. Support any groups that are finding it hard to start. Do not lead them through the process, but one suggestion is to identify the top ten female tennis players, find their fastest service speeds and their height, and then process that information. The teacher should group- teach any concept that the students might need in order to help them to proceed, e.g. after encouraging the use of measuring correlation via the shortest perpendicular distances, lead the students on to Spearman’s Rank correlation. It is important that the formula is dissected to enable the students to get a feel for the various elements. Extend to both genders and then compare the correlation if it exists. Aim to extend to the product moment correlation coefficient and the linear regression model for predictions, e.g. if you are 6 feet 11 inches tall… (deliberate use of imperial measurements).

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Resources/documentation

Learners require access to the internet and basic equipment including a scientific calculator. The use of the Casio Fx991 is recommended here. Use of a spreadsheet for all the calculations.

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Possible extensions

  • Product moment correlation coefficient and the linear regression model.
  • Testing between the correlations by comparing with critical values in statistical tables.
  • Extend the hypothesis to a related but different aspect in another sport – with the speed/height of a fast bowler being the obvious example.

Further additional materials are provided by a plethora of internet sites including:

http://twu.tennis-warehouse.com/learning_center/kickserve.php http://www.bbc.co.uk/sport/tennis

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Acknowledgement

Developed for Core Maths by Colin Prestwich of the Yorkshire Ridings Maths Hub. Materials reviewed by Will Rigby.