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© Boardworks Ltd of 38 D4 Moving averages and cumulative frequency Maths Age 14-16

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© Boardworks Ltd of 38 Contents A A A A A D4.5 Box-and-whisker diagrams D4 Moving averages and cumulative frequency D4.3 Cumulative frequency D4.2 Plotting moving averages D4.1 Moving averages D4.4 Using cumulative frequency graphs

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© Boardworks Ltd of 38 A box-and-whisker diagram A box-and-whisker diagram, or boxplot, can be used to illustrate the spread of the data in a given distribution using the highest and lowest values, the median, the lower quartile and the upper quartile. These values can be found from a cumulative frequency graph. Time in seconds Cumulative frequency For example, for this cumulative frequency graph showing the results of 100 people holding their breath, Minimum value = 30 Lower quartile = 42 Median = 47 Upper quartile = 51 Maximum value = 60

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© Boardworks Ltd of 38 A box-and-whisker diagram The corresponding box-and-whisker diagram is as follows: 30 Minimum value 42 Lower quartile 47 Median 51 Upper quartile 60 Maximum value

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© Boardworks Ltd of 38 Lap times James takes part in karting competitions and his Dad records his lap times on a spreadsheet. The track is 1108 metres long. James’ fastest time in a race was 51.8 seconds. In which position in the list would the median lap time be? In 2004, 378 of James’ lap times were recorded. There are 378 lap times and so the median lap time will be the th value ≈ 190 th value

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© Boardworks Ltd of 38 Lap times In which position in the list would the lower quartile be? There are 378 lap times and so the lower quartile will be the th value ≈ 95 th value In which position in the list would the upper quartile be? There are 378 lap times and so the upper quartile will be the 284 th value th value ≈ 3 ×

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© Boardworks Ltd of 38 Lap times at Shenington karting circuit James’ lap times are displayed in the following cumulative frequency graph. Lap times in seconds Cumulative frequency

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© Boardworks Ltd of 38 Box and whisker plot for James’ race times What conclusions can you draw about James’ performance? 52 Minimum value 53 Lower quartile 54 Median 58 Upper quartile 91 Maximum value

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© Boardworks Ltd of 38 Comparing sets of data Here are box-and-whisker diagrams representing James’ lap times and Shabnum’s lap times. Who is better and why? James’ lap times Shabnum’s lap times

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