Answers

1.  
   1. This is a continuous variable. Return to exercise 1a
   2. This is a discrete variable. Return to exercise 1b
   3. This is a discrete variable. Return to exercise 1c
   4. This is a continuous variable. Return to exercise 1d
   5. This is a continuous variable. Return to exercise 1e
   6. This is a discrete variable. Return to exercise 1f
   7. This is a continuous variable. Return to exercise 1g
   8. This is a continuous variable (this could also be considered discrete). Return to exercise 1h
   9. This is a discrete variable. Return to exercise 1i
   10. This is a discrete variable. Return to exercise 1j
   11. This is a continuous variable. Return to exercise 1k
   12. This is a discrete variable. Return to exercise 1l
2. There are various answers to this question. Return to exercise 2
3.  
   1.  
      

      Answers to question 3a

      Number of telephones (x)	Tally	Frequency (f)
      1		1
      2		2
      3		5
      4		3
      5		1
      Total		12

      Return to exercise 3a
   2. The number 3 occurs the most frequently. Return to exercise 3b
4.  
   1. These are discrete variables. Return to exercise 4a
   2.  
      

      Answers to question 4b

      Number of customers (x)	Tally	Frequency (f)
      20		2
      21		7
      22		4
      23		3
      24		5
      25		2
      26		2
      Total		25

      Return to exercise 4b
   3. The observation that occurs the most frequently is 21. Return to exercise 4c
   4.  
      

      Answers to question 4d

      Number of customers (x)	Frequency (f)	Relative frequency	Percentage frequency
      20	2	0.08	8
      21	7	0.28	28
      22	4	0.16	16
      23	3	0.12	12
      24	5	0.20	20
      25	2	0.08	8
      26	2	0.08	8
      Total	25	1.00	100

      Return to exercise 4d
5.  
   1. These are continuous variables. Return to exercise 5a
   2.  
      

      Answers to question 5b

      Wind speed (x)	Tally	Frequency (f)
      0 to < 5		3
      5 to < 10		4
      10 to < 15		14
      15 to < 20		11
      20 to < 25		7
      25 to < 30		0
      30 to < 35		1
      Total		40

      Return to exercise 5b
   3. The class interval that appears the most frequently is 10 –< 15. Return to exercise 5c
   4.  
      

      Answers to question 5d

      Wind speed (x)	Frequency (f)	Relative frequency	Percentage frequency
      0 to < 5	3	0.075	7.5
      5 to < 10	4	0.100	10.0
      10 to < 15	14	0.350	35.0
      15 to < 20	11	0.275	27.5
      20 to < 25	7	0.175	17.5
      25 to < 30	0	0.000	0.0
      30 to < 35	1	0.025	2.5
      Total	40	1.000	100.0

      Return to exercise 5d
   5. The most commonly occurring wind speed is from 10 to less than 15 knots. Based on this 40-day sample, this wind speed has a 35% chance of occurring on any given day. Return to exercise 5e
6.  
   1.  
      

      Answers to question 6a

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

      Return to exercise 6a
   2. The outlier in this exercise is the number 34. Possible explanations:
      • a particularly windy or stormy day that took place during the 40 days
      • there was a measurement error
      Return to exercise 6b
   3.  
      1. The distribution has only one main peak.
      2. The distribution is roughly asymmetrical. If the outlier were removed, it would be roughly skewed to the left. Generally, the distribution takes an irregular shape.
      3. The centre of distribution is 14 knots.
      Return to exercise 6c
7.  
   1.  
      

      Answers to question 7a

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

      Return to exercise 7a
   2.  
      

      Answers to question 7b

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

      Return to exercise 7b
8.  
   1. These are discrete variables. Return to exercise 8a
   2.  
      

      Answers to question 8b

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

      Return to exercise 8b
   3.  
      

      Answers to question 8c

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

      Return to exercise 8c
   4. No outliers exist in this exercise. Return to exercise 8d
   5.  
      1. The distribution has only one main peak.
      2. The general shape of the distribution is skewed to the left.
      3. The approximate value at the centre of the distribution is 28 road fatalities.
      Return to exercise 8e
9.  
   1. These are continuous variables. Return to exercise 9a
   2.  
      

      Answers to question 9b

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

      Return to exercise 9b
   3. No, it is not necessary to expand the stem and leaf plots because the stems are not overcrowded. Return to exercise 9c
   4. There are no outliers. Return to exercise 9d
   5.  
      1. The distribution has one main peak.
      2. The general shape of the distribution is roughly symmetric (although this is difficult to observe with such a small amount of data).
      3. The centre of distribution is 7 °C.
      Return to exercise 9e
10.  
    1. These are discrete variables. Return to exercise 10a
    2.  
       

       Answers to question 10b

       Weekly salary (x)	Tally	Frequency (f)
       420 to < 440		1
       440 to < 460		4
       460 to < 480		14
       480 to < 500		9
       500 to < 520		8
       520 to < 540		8
       540 to < 560		5
       560 to < 580		1
       Total		50

       Return to exercise 10b
    3. The class interval that occurs the most frequently is $460–<480. Return to exercise 10c
    4.  
       

       Answers to question 10d

       Weekly salary (x)	Frequency (f)	Relative frequency	Percentage frequency
       420 to < 440	1	0.02	2
       440 to < 460	4	0.08	8
       460 to < 480	14	0.28	28
       480 to < 500	9	0.18	18
       500 to < 520	8	0.16	16
       520 to < 540	8	0.16	16
       540 to < 560	5	0.10	10
       560 to < 580	1	0.02	2
       Total	50	1.00	100

       Return to exercise 10d
    5. The most common salary group, representing 28% of the employees is between $460 and $480 a week based on this sample of 50 people. Only one staff member earned over $560 a week. Return to exercise 10e
    6.  
       

       Answers to question 10f

       Stem	Leaf
       43	7
       44	0 1 3
       45	9
       46	1 1 3 3 6 6
       47	0 0 0 1 3 3 6 8
       48	1 4 4 6 6 7
       49	0 7 9
       50	2
       51	1 3 4 4 7 9 9
       52	2 3 3 5 7 8
       53	9
       54	2 3 6 8
       55	5
       56	4

       Return to exercise 10f
    7. There are no outliers. If there were outliers a possible explanation for them could be:
       • these people may have been managers or directors and thus on higher salaries
       • these people may have given misleading responses.
       Return to exercise 10g
    8.  
       1. The distribution has many peaks which indicated the possibility of being bimodal.
       2. The distribution is neither symmetrical nor is it skewed.
       3. The centre of the distribution is between $487 and $490.
       Return to exercise 10h