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Objective 1 9.6 Box-and-Whisker Plots Draw a box-and-whisker plot to organize real-life data. Read and interpret a box-and-whisker plot of real-life data. Objective 2

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The median or second quartile separates the set into two halves, the numbers that are below the median and the numbers that are above the median. The first quartile is the median of the lower half. The third quartile is the median of the upper half. The “box” extends from the first to the third quartile. The “whiskers” connect the box to the least and greatest numbers. A box-and-whisker plot is a data display that divides a set of data into four parts.

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Find the quartiles Find the values of the whiskers Draw a box plot to scale – on graph paper Stages in drawing a box plot

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles (b) Draw a box-and-whisker plot to represent these data

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles (b) Draw a box-and-whisker plot to represent these data

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles (b) Draw a box-and-whisker plot to represent these data

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data:

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data:

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data: 1 1 3 4 4 5 6 9 10 18 The median is the middle value: Q2

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data: 1 1 3 4 4 5 6 9 10 18 The median is the middle value: = 4.5 mins The lower quartile, Q1 3rd value Q2

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data: 1 1 3 4 4 5 6 9 10 18 The median is the middle value: = 4.5 mins The lower quartile, Q1 3 mins 3rd value = Q1Q2

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data: 1 1 3 4 4 5 6 9 10 18 The median is the middle value: = 4.5 mins The lower quartile, Q1 3 mins The upper quartile, Q3 8 th value = Q1Q2

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data: 1 1 3 4 4 5 6 9 10 18 The median is the middle value: = 4.5 mins The lower quartile, Q1 3 mins The upper quartile, Q3 8 th value = 9 mins Q1Q3Q2

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Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (a) Find the quartiles Answer re-order the data: 1 1 3 4 4 5 6 9 10 18 The median is the middle value: = 4.5 mins The lower quartile, Q1 3 mins The upper quartile, Q3 9 mins The “box” inter-quartile range = Q3 – Q1 = 9 – 3 = 6 mins Q1Q3Q2

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Answer: Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (b) Draw a box-and-whisker plot to represent these data 1 1 3 4 4 5 6 9 10 18 Q1Q3 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 0510152025 1 1 3 4 4 5 6 9 10 18 Q1Q3Q2

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Answer: Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (b) Draw a box-and-whisker plot to represent these data 1 1 3 4 4 5 6 9 10 18 Q1Q3 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 0510152025 1 1 3 4 4 5 6 9 10 18 Q1Q3Q2

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Answer: Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (b) Draw a box-and-whisker plot to represent these data 1 1 3 4 4 5 6 9 10 18 Q1Q3 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 0510152025 1 1 3 4 4 5 6 9 10 18 Q1Q3Q2

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Answer: Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (b) Draw a box-and-whisker plot to represent these data 1 1 3 4 4 5 6 9 10 18 Q1Q3 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 0510152025 1 1 3 4 4 5 6 9 10 18 Q1Q3Q2

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Answer: Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (b) Draw a box-and-whisker plot to represent these data 1 1 3 4 4 5 6 9 10 18 Q1Q3 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 0510152025 1 1 3 4 4 5 6 9 10 18 Q1Q3Q2

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Answer: Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (b) Draw a box-and-whisker plot to represent these data 1 1 3 4 4 5 6 9 10 18 Q1Q3 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 0510152025 1 1 3 4 4 5 6 9 10 18 Q1Q3Q2

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Answer: Example: Waiting times at a bus were recorded, to the nearest minute, on 10 occasions. The data collected were: 6, 1, 4, 9, 18, 3, 5, 10, 1, 4 (b) Draw a box-and-whisker plot to represent these data 1 1 3 4 4 5 6 9 10 18 Q1Q3 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 1 1 3 4 4 5 6 9 10 18 Q1Q3Q2 0510152025

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0510152025 Using just the box-and-whisker plot, compare the number of people who waited 1 to 3 minutes to the number of people who waited 9 to 18 minutes. The numbers are about the same because each whisker represents about 25% of the data. Answer: Example: Read and interpret a box-and-whisker plot. How long is the median wait time for the bus? The median wait time is 4.5 minutes.Answer: Bus wait time

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