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Exercises

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  1. Indicate whether each of the following variables is discrete or continuous:
    1. the time it takes for you to get to school Answer 1a
    2. the number of Canadian couples who were married last year Answer 1b
    3. the number of goals scored by a women’s hockey team Answer 1c
    4. the speed of a bicycle Answer 1d
    5. your age Answer 1e
    6. the number of subjects your school offered last year Answer 1f
    7. the length of time of a telephone call Answer 1g
    8. the annual income of an individual Answer 1h
    9. the number of employees at Statistics Canada Answer 1i
    10. the number of brothers and sisters you have Answer 1j
    11. the distance between your house and school Answer 1k
    12. the number of pages in a dictionary Answer 1l
  2. Without using any of the examples from question 1, give two examples of: Answer 2
    1. a discrete variable
    2. a continuous variable
  3. A telephone company surveyed 12 households to find out how many telephones there were per household.
    1. Copy the frequency distribution table below into your notebook and complete it using the following survey results:

      2, 5, 4, 3, 4, 3, 1, 3, 3, 2, 3, 4 Answer 3a

      Question 3a
      Number of telephones (x) Tally Frequency (f)
      1    
      2    
      3    
      4    
      5    
    2. Which result occurs most frequently? Answer 3b
  4. A local convenience store owner records how many customers enter the store each day over a 25-day period. The results are as follows:

    20, 21, 23, 21, 26, 24, 20, 24, 25, 22, 22, 23, 21, 24, 21, 26, 24, 22, 21, 23, 25, 22, 21, 24, 21

    1. Are these discrete or continuous variables? Answer 4a
    2. Present these data in a frequency distribution table. Answer 4b
    3. Which result occurs most frequently? Answer 4c
    4. Set up a frequency distribution table including columns for the relative frequency and percentage frequency of the data. Answer 4d
    5. What conclusions can you draw from the tables? Explain.
  5. A wind blew for 40 days. Its wind speeds, in knots, were recorded as follows:

    15, 22, 14, 12, 21, 34, 19, 11, 13, 0, 16, 4, 23, 8, 12, 18, 24, 17, 14, 3, 10, 12, 9, 15, 20, 5, 19, 13, 17, 11, 16, 19, 24, 12, 7, 14, 17, 10, 14, 23

    1. Are these discrete or continuous variables? Answer 5a
    2. Choose an appropriate class interval and present these data in a frequency distribution table. Answer 5b
    3. Which class interval occurs most frequently? Answer 5c
    4. Set up a frequency distribution table including columns for the relative frequency and percentage frequency of the data.Answer 5d
    5. What conclusions can be drawn from the tables? Explain. Answer 5e
  6.  
    1. Prepare an ordered stem and leaf plot for the data in Exercise 5. Answer 6a
    2. Do any outliers exist? If so, give a reason for their presence. Answer 6b
    3. Describe the main features of the distribution:Answer 6c
      1. number of peaks
      2. general shape
      3. approximate value at the centre of the distribution
  7. Thirty people were surveyed to find out how often they went to the movie theatre in one year. The results are as follows:

    21, 35, 27, 2, 18, 25, 10, 4, 43, 14, 29, 24, 15, 9, 26, 31, 41, 1, 28, 38, 40, 22, 37, 26, 19, 0, 33, 12, 16, 23

    1. Copy the stem and leaf plot below into your notebook and complete it for the results. Answer 7a
      Question 7a
      Stem Leaf
      0  
      1  
      2  
      3  
      4  
    2. Now, turn the plot into an ordered stem and leaf plot. Answer 7b
  8. Assume the annual numbers of road fatalities from 1960 to 1992 were as follows:

    10, 7, 8, 8, 17, 15, 17, 23, 14, 26, 31, 20, 32, 29, 31, 32, 38, 29, 30, 24, 30, 29, 26, 28, 37, 33, 32, 36, 32, 32, 26, 17, 20

    1. Are these discrete or continuous variables? Answer 8a)
    2. Prepare an ordered stem and leaf plot of these data.Answer 8b
    3. Expand the stem and leaf plot by using five-unit class intervals. Answer 8c
    4. Do any outliers exist? If so, give a reason for their presence. Answer 8d
    5. Describe the main features of the distribution:Answer 8e
      1. number of peaks
      2. general shape
      3. approximate value at the centre of the distribution
  9. From 1982 to 2002, the average minimum April temperature (Celsius) was recorded as follows:

    6,1, 8,9, 6,9, 7,2, 7,0, 6,2, 5,7, 6,2, 6,8, 6,4, 6,8, 6,4, 7,6, 7,8, 7,3, 6,8, 8,8, 7,8, 8,1, 8,1, 7,9

    1. Are these discrete or continuous variables? Answer 9a
    2. Prepare an ordered stem and leaf plot for this data. Answer 9b
    3. Is it necessary to expand the stem and leaf plot? Why or why not?Answer 9c
    4. Do any outliers exist? If so, give a reason for their presence. Answer 9d
    5. Describe the main features of the distribution. Answer 9e
      1. number of peaks
      2. general shape
      3. approximate value at the centre of the distribution
  10. Fifty staff members of a construction company were surveyed to find out what their weekly salary was to the nearest dollar. The results are as follows:

    514, 476, 497, 511, 484, 513, 471, 470, 441, 466, 443, 481, 502, 528, 459, 548, 521, 517, 463, 478, 473, 514, 542, 519, 522, 523, 546, 487, 486, 473, 527, 470, 440, 564, 499, 523, 484, 463, 461, 437, 555, 525, 461, 539, 466, 470, 486, 490, 543, 519

    1. Are these discrete or continuous variables? Answer 10a
    2. Choose an appropriate class interval and present these data in a frequency distribution table. Answer 10b
    3. Which class interval occurs most frequently? Answer 10c
    4. Set up a frequency distribution table including columns for the relative frequency and percentage frequency of the data.Answer 10d
    5. What conclusions can you draw from the tables? Explain.Answer 10e
    6. Prepare an ordered stem and leaf plot for this data. Answer 10f
    7. Do any outliers exist? If so, can you give a reason for their presence? Answer 10g
    8. Looking at the stem and leaf plot, describe the main features of the distribution:Answer 10h
      1. number of peaks
      2. general shape
      3. approximate value at the centre of the distribution

Class activities

  1. Draw a straight line exactly 10 centimetres (cm) in length. Without measuring, place a mark where you estimate the halfway point to be. Now measure the line, and place a mark at the actual halfway point (5 cm). Measure the distance between your estimate and the actual halfway point. How many millimetres (mm) was your estimate short of the halfway point?
    1. Record this value in a table. Find out how far the rest of the class deviated from the halfway point and record these results.
    2. With these data, construct a frequency distribution table including columns for relative frequency and percentage frequency of the data.
    3. Which result occurs most frequently?
    4. Prepare a stem and leaf plot for this data.
    5. Do any outliers exist? If so, give a reason for their presence.
    6. Describe the main features of the distribution:
      1. number of peaks
      2. general shape
      3. approximate value at the centre of the distribution
    7. What conclusions can you draw from this analysis?
  2. Ask your teacher for the class results (anonymous) from a recent test or assignment. Perform a detailed analysis on these data using the instructions described in a) to g) of Class activities 1. Briefly comment on:
    1. the class average of the test or assignment
    2. the ability of the class to understand the test or assignment questions
    3. the interest the class appears to have in the material tested

    Support each answer with evidence based on your analysis.

  3. Throw one die 30 times. Using a frequency distribution table, record the result of each throw.
    1. Are these discrete or continuous variables?
    2. Set up a frequency distribution table including columns for the relative frequency and percentage frequency of the data.
    3. What result occurs most frequently?
    4. Did you expect any number to occur more often than the others? If so, why?
    5. Prepare a stem and leaf plot for these data.
    6. Do any outliers exist? If so, give a reason for their presence.
    7. Describe the main features of the distribution:
      1. number of peaks
      2. general shape
      3. approximate value at the centre of the distribution
    8. What conclusions can you draw from the analysis?
  4. Create a table listing primary and secondary colours: red, blue, yellow, purple, green and orange. Include black, white, and grey as well. Do not include complementary shades of colours (blue-green, mauve, beige, etc.) in your table. Finally, label the last column "None of these colours".

    Then survey the teachers in your school to find out what colour car they drive. If a teacher responds with a colour that is not on your table, record their answer in the "None of these colours" column.
    1. Are these discrete or continuous variables?
    2. Set up a frequency distribution table including columns for the relative frequency and percentage frequency of the data.
    3. Determine which car colour is the most popular among the surveyed teachers. By what percentage is this colour more popular than the second most common colour?
    4. Why is it impossible to prepare a stem and leaf plot for this data?
    5. Why might a car manufacturer want this type of data analysis?