Answers

1.  
   1.  
      

      Table 1. Number of years of reign for English monarchs

      Stem	Leaf	Frequency (f)	Upper Value	Cumulative frequency	Cumulative percentage
      0	0 0 1 1 2 3 5 5 7 7 9 9	12	9	12	28.57
      1	0 0 2 3 3 3 4 5 8 8	10	18	22	52.23
      2	0 2 2 2 3 4 4 5 6	9	26	31	73.80
      3	3 4 4 5 8 9	6	38	37	88.09
      4	4	1	44	38	90.47
      5	0 6 9	3	59	41	97.61
      6	4	1	64	42	100.00

      Return to question 1a
   2. The possible outliers are 56, 59 and 64. However, this data is based on fact, so the numbers exist because each of these monarchs came to the throne early in their youth and enjoyed long lives. This reasoning suggests that there are no outliers. Return to question 1b
   3.  
      • The number of peaks that appear at the beginning of the distribution is one.
      • The general shape of the distribution is skewed to the right.
      • The approximate value at the centre of the distribution is 18 years.
      Return to question 1c
   4. Same answer of table 1 Return to question 1d
   5.  
      
      Return to question 1e
   6.  
      • There are 12 monarchs who have reigned for less than 10 years.
      • There are 4 monarchs who have reigned for 50 years or more.
      Return to question 1f
   7. Queen Elizabeth II celebrated her 58th year of rulership on February 6, 2010. Her reign is already well above the centre of distribution and only two other monarchs have been on the throne longer. Return to question 1g
2.  
   1.  
      

      Table 2. Number of french fries per small bag

      Stem	Leaf
      2(0)	1
      2(5)
      3(0)	1 2 4
      3(5)	5 7 7 8 8
      4(0)	0 0 2 3 3 3 4
      4(5)	5 5 6 6 7 7 8 9
      5(0)	0 1 4 4
      5(5)

      Return to question 2a
   2. The outlier in this exercise is 21. One reason could be that there were only 21 fries in the bag on that day because they were the only fries left in the batch. Another reason could be that the number recorded was incorrect (i.e., 21 instead of 41). Return to question 2b
   3.  
      • The graph is unimodal, meaning it has only one peak in this distribution.
      • If the outlier is removed, the general shape of the distribution is roughly symmetric.
      • The approximate value at the center of distribution is between 43 and 44 or 43.5 fries.
      Return to question 2c
   4.  
      

      Table 3. Number of french fries per small bag

      Number of fries	Frequency (f)	Upper value	Cumulative frequency	Cumulative percentage
      20 to 24	1	21	1	3.3
      25 to 29	0	29	1	3.3
      30 to 34	3	34	4	13.3
      35 to 39	5	38	9	30.0
      40 to 44	7	44	16	53.3
      45 to 49	8	49	24	80.0
      50 to 54	4	54	28	93.3
      55 to 59	2	59	30	100.0
      Total	30			100.0

      Note: If you have a class interval that is empty, you should always use the endpoint as the upper value. For instance, in the above example, there is one bag in the 20–24 interval, but no bags in the 25–29 interval. To determine the upper value for the 25–29 interval, use the endpoint of 29. Return to question 2d

   5.  
      
      Return to question 2e
   6.  
      • In 30 bags of french fries, only 9 had fewer than 40 fries in them.
      • The percentage of bags with 45 or more fries is 46.7%.
      Return to question 2f
   7. The promotional slogan should read: "Our bags may be small but half contain at least 44 french fries!" Return to question 2g
3.  
   1. These are continuous variables. Return to question 3a
   2.  
      

      Table 4. Number of unemployed female job-seekers, by age group

      Age group	Number of females	Endpoint	Cumulative frequency	Cumulative percentage
      0 to 14	0	15	0	0.0
      15 to 24	339	25	339	37.6
      25 to 34	273	35	612	67.8
      35 to 44	147	45	759	84.1
      45 to 54	121	55	880	97.6
      55 to 64	22	65	902	100.0

      Return to question 3b
   3.  
      
      Return to question 3c
   4. There is no data for females under 15 years of age because no one under 15 can be classified as unemployed. Return to question 3d
   5. The cumulative percentage of 50% falls within the age group of 25–34 (approximately 29 years old). Return to question 3e
   6. The percentage of unemployed females who are under 25 years of age and looking for full-time work is 37.6%. Return to question 3f
   7. The percentage of unemployed females who are 55 years and older and looking for full-time work is 2.4%. Return to question 3g
   8. The Canadian government could establish job-creation schemes directed at particular age groups. In this case, the job-creation scheme would likely be for those under 25 years of age. Return to question 3h
4.  
   1. These are continuous variables. Return to question 4a
   2.  
      

      Table 5. Commuter time of Statistics Canada employees, Ottawa

      Time (x)	Tally	Frequency (f)	Relative frequency	Relative percentage
      0 to < 10		0	0.00	0
      10 to < 20		1	0.02	2
      20 to < 30		3	0.06	6
      30 to < 40		4	0.08	8
      40 to < 50		7	0.14	14
      50 to < 60		10	0.20	20
      60 to < 70		15	0.30	30
      70 to < 80		5	0.10	10
      80 to < 90		4	0.08	8
      90 to < 100		1	0.02	2
      Total		50	1.00	100

      Return to question 4b
   3.  
      
      Return to question 4c
   4.  
      

      Table 6. Commuter time of Statistics Canada employees, Ottawa

      Stem	Leaf
      0
      1	2
      2	2 5 9
      3	1 3 7 8
      4	0 1 3 4 5 5 9
      5	0 1 2 2 5 6 6 8 8 9
      6	0 0 1 2 3 3 4 4 5 5 6 7 8 9 9
      7	1 3 5 6 7
      8	0 3 7 9
      9	8

      A possible outlier could be 98. The reason for this outlier might be that the person had difficulty in getting to work, or simply lives further away than most employees. Return to question 4d

   5.  
      • The graph is unimodal, meaning it only has one peak in the distribution.
      • The general shape at the centre of distribution is quite symmetric.
      • The approximate value at the centre of distribution is between 59 and 60 or 59.5 minutes.
      Return to question 4e
   6.  
      

      Table 7. Commuter time of Statistics Canada employees, Ottawa

      Time (x)	Frequency (f)	Endpoint	Cumulative frequency	Cumulative percentage
      0 to < 10	0	10	0	0
      10 to < 20	1	20	1	2
      20 to < 30	3	30	4	8
      30 to < 40	4	40	8	16
      40 to < 50	7	50	15	30
      50 to < 60	10	60	25	50
      60 to < 70	15	70	40	80
      70 to < 80	5	80	45	90
      80 to < 90	4	90	49	98
      90 to < 100	1	100	50	100

      Return to question 4f
   7.  
      
      Return to question 4g
   8.  
      • The most common time interval for Statistics Canada employees to get to work in is 60 –< 70 minutes.
      • Only 2% of employees take more than 90 minutes to travel to work.
      • Out of the 50 employees surveyed, only 8 took less than 40 minutes to travel to work.
      Return to question 4h