Box & Whisker plots

5 figure summary	1. Determine the 5 figure summary for the following data set of 9 observations: 3, 5, 7, 2, 6, 3, 4, 6, 7. Answer.[2, 3, 5, 6.5,7].
	2. Determine the 5 figure summary for the following data set: 1, 1, 2, 5, 7, 9, 10, 10, 11, 11, 12, 13. Answer.[1, 3.5, 9.5, 11, 13].
	3. The five figure summary for a data set is: [2, 3, 7, 11, 12] Which of the following data sets could have been used to create the above summary? (a) 2, 3, 5, 9, 11, 12. (b) 2, 3, 7 ,7, 10, 12. (c) 2, 3, 4, 7, 11, 12, 12. (d) 2, 3, 6, 7, 10, 12, 12. Answer.(a).
	4. In a five-number summary of the following data set, what is the entry indicating the upper quartile 20, 22, 25, 28,36, 40, 40, 42, 46 Answer.Q3 is 41.
Drawing from a 5 figure summary.	5. Draw a box plot from the following 5 figure summary: [1, 4, 6, 11, 14].
	6. Draw a box and whisker plot from the following 5 figure summary:
Drawing from a data set.	7. A data set is 1, 3, 4, 4, 4, 5, 6, 6, 7, 8, 9. (i) Prepare a five figure summary of this data set. (ii) Draw a box and whisker plot. Answer.(i) [2, 4, 5, 7, 9].
	8. A data set is 25, 15, 17, 10, 18, 19, 12, 17, 18, 14. (i) Prepare a five figure summary of this data set. (ii) Draw a box and whisker plot. Answer.(i) [10, 14, 17, 18, 25].
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Interpreting a single plot.	10. The following box plot summarises the results of an assessment given to 120 students. Which of the following statements are correct? Give a reason to support your answer. (i) The median score is 40. (ii) 30 students scored less than 46. (iii) 120 students scored 47 or more. (iv) 60 students scored 40 or more. (v) The number of students scoring 46 or more is equal to the number scoring 38 to 46. Answer.(i) Correct the median is 40 as shown by the vertical line inside the box. (ii) Incorrect - 46 marks (Q3) is where 75% of students are accounted for. So the number up to 46 is 90 students. (iii) Incorrect - 120 students (all) scored 34 or more. (iv) Correct - half the 120 students (60) scored at the median (40) or more. (v) Incorrect - 25% of students (30) scored 46 or more while 50% of students (50) scored 38 to 46 (which is the inter-quartile range).
	11. A local Post Office handled 12,000 small parcels in one week. Small parcels are defined as being less than 5 kg. The box and whisker plot below summarises the weights of these parcels. How many of the parcels handled by this Post Office in that week weighed between 1.0 kg and 2 kgs? Answer.25% of 12,000 = 3,000 parcels.
	12. From the following box-plot, what percentage of observations: (i) lie between 10 and 25? (ii) lie between 45 and 80? (iii) are greater than 25? (iv) are less than 80 but greater than 50? Answer.(i) 25% (ii) 50%. (iii) 75%. (iv) 25%.
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Interpreting parallel box plots.	14. The box and whisker plots above show the distribution of the ages of children attending the NSS Education Centre in 2010 and 2020. In 2010, the centre accommodated 1200 students aged 0 (in the creche) to age 18 (HSC level). (I) How many students aged 16 to 18 years were there in 2010? (ii) How many students were there attending the Centre in 2020 given that the number of students in 2010 aged 6 to 18 equalled the number of students in 2020 aged over 16? (iii) How many students less than 6 years attended the pre-school of the Educational Centre in 2020? (iii) What conclusion can you make by comparing the median ages of each group?
	15. The box plot shown below summaries the waiting time (in minutes) for a group of people who are to receive their first COVID-19 injection. (i) In this group, 60 females were waiting for their injection. An equal number of females and males waited for 13 minutes or less. How many males were waiting for their injection? (ii) Compare the waiting time for females and males by using the results for measures of spread and the distribution shape. Answer.(i) 30 males.
	16. The box plot below summarises the age of passengers in two airport departure lounges who were taking their first flight. Luke and Leah both walked around the lounges surveying the passengers. Luke collected information from 80 passengers in Lounge 3 while Leah collected the data from a number of passengers in Lounge 4. (i) What was the age of the oldest passenger taking their first flight and in what Lounge were they sitting? (ii) How old was the youngest passenger taking their first flight and in what Lounge were they sitting? (iii) How many people in Lounge 3 were taking their first flight and aged less than 17 years? (iv) If the number of people in Lounge 5 aged 22 to 25 was the same number as those aged over 23 in Lounge 3, how many people were surveyed in Lounge 5? Answer.(i) Aged 29 sitting in Lounge 5. (ii) Aged 9 sitting in Lounge 3. (iii) 20 passengers. (iv) 160 passengers.