Hot shot – a question of consistency

This is a precursor to the linked tasks of Due date, Baby boom and Chicken and egg, on the Normal distribution. It introduces the need for a measure of spread related to the mean leading to the variance and standard deviation.

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Overview of task

This is a precursor to the linked tasks of Due date, Baby boom and Chicken and egg, on the Normal distribution. It introduces the need for a measure of spread related to the mean leading to the variance and standard deviation.

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Strand

Statistics

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Prior knowledge

Students need to be familiar with the statistics: median and mean.

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Relevance to Core Maths qualifications

•AQA

•C&G

•Eduqas

•Pearson/Edexcel

•OCR

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Suggested approaches

This is a whole class task with opportunity for group investigation, as it starts with a problem about who is the ‘best’ shot. The data is contrived to have the same mean and median.

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Resources/documentation

There is a PowerPoint presentation, a handout of results (available in Word or as a pdf) and interactive whiteboard resources.

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Relevant digital technologies

Students will need to use calculators to compute the variance and standard deviation. Calculators with suitable statistics functionality could be used to illustrate how these values can be determined for any set of data.

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Possible extensions

Generating their own experimental data and investigating the standard deviation as a measure of spread – possibly comparing with the interquartile range which can be easily understood.

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Acknowledgement

Developed by Derek Robinson for the CMSP.