Objective 1

1. Objective 1 Objective 2 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.

2. A box-and-whisker plot is a data display that divides a set of data into four parts. • 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.

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

4. 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

5. 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

6. 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

7. 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:

8. 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 Answerre-order the data:

9. 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 Q2 The median is the middle value:

10. 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 Q2 The median is the middle value: = 4.5 mins The lower quartile, Q1  3rd value

11. 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 Q1 Q2 The median is the middle value: = 4.5 mins The lower quartile, Q1  3rd value = 3 mins

12. 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 Q1 Q2 The median is the middle value: = 4.5 mins 3 mins The lower quartile, Q1 The upper quartile, Q3  8th value =

13. 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 Q1 Q2 Q3 The median is the middle value: = 4.5 mins The lower quartile, Q1 3 mins The upper quartile, Q3  8th value = 9 mins

14. 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 Q1 Q2 Q3 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

15. 1 1 3 4 4 5 6 9 10 18 Q1 Q2 Q3 0 5 10 15 20 25 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 Answer: 1 1 3 4 4 5 6 9 10 18 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 Q1 Q3

16. 1 1 3 4 4 5 6 9 10 18 Q1 Q2 Q3 0 5 10 15 20 25 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 Answer: 1 1 3 4 4 5 6 9 10 18 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 Q1 Q3

17. 1 1 3 4 4 5 6 9 10 18 Q1 Q2 Q3 0 5 10 15 20 25 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 Answer: 1 1 3 4 4 5 6 9 10 18 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 Q1 Q3

18. 1 1 3 4 4 5 6 9 10 18 Q1 Q2 Q3 0 5 10 15 20 25 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 Answer: 1 1 3 4 4 5 6 9 10 18 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 Q1 Q3

19. 1 1 3 4 4 5 6 9 10 18 Q1 Q2 Q3 0 5 10 15 20 25 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 Answer: 1 1 3 4 4 5 6 9 10 18 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 Q1 Q3

20. 1 1 3 4 4 5 6 9 10 18 Q1 Q2 Q3 0 5 10 15 20 25 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 Answer: 1 1 3 4 4 5 6 9 10 18 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 Q1 Q3

21. 1 1 3 4 4 5 6 9 10 18 Q1 Q2 Q3 0 5 10 15 20 25 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 Answer: 1 1 3 4 4 5 6 9 10 18 Recall from (a) Q1 = 3, Q2 = 4.5, Q3 = 9 Q1 Q3

22. 0 5 10 15 20 25 Example: Read and interpret a box-and-whisker plot. Bus wait time 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. Answer: The numbers are about the same because each whisker represents about 25% of the data. How long is the median wait time for the bus? Answer: The median wait time is 4.5 minutes.