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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
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.
5.

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.
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)
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.
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.

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%.
7. The promotional slogan should read: "Our bags may be small but half contain at least 44 french fries!" Return to question 2g
3.
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
3.

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.
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
3.

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.
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