BC Math 9 Statistics in Society

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  • Population versus sample, bias, ethics, sampling techniques, misleading stats
  • Analyzing a given set of data (and / or its representation) and identifying potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity
  • Using First Peoples data on water quality, Statistics Canada data on income, health, housing, population
  1. What is the mean of 2, 4, and 9?
    Solution
    5
  2. What is the average of 1, 3, 8, and 20?
    Solution
    8
  3. 2, 5, k
    Given the mean is 6, find k
    Solution
    11
  4. 1, 2, 11, n
    Given the average is 7, find n
    Solution
    14
  5. Find the median of the following numbers:
    1. 1, 2, 4, 10, 50, 1000, 999999?
      Solution
      10
    2. 2, 10, 20, 5000?
      Solution
      15
    3. -5, 1, 2, 100
      Solution
      1.5
    4. -1000, 500, 100, 200
      Solution
      150
    5. -20, 0, 100, 50, -1000
      Solution
      0
  6. When conducting a survey, why do we poll a sample instead of the entire population?
  7. Solution
    It is not realistic to poll everyone.  It costs too much and takes too much time.
  8. Give an example of statistical bias.
    Solution
    If you poll rural areas only, citizens may be less likely to support increased Translink funding. Also, a community may be in poorer health due to a lack of clean drinking water.
  9. Is it ethical to misrepresent data in statistical research?  Why are some researchers tempted to do so?
    Solution
    No.  Researchers sometimes want the data to support their hypothesis to show that have produced a breakthrough. Researchers may also be tempted to produce results in support their ongoing funding.
  10. Why did Mark Twain write “There are lies, damn lies, and statistics.”  To answer this research the phrase “how can statistics lie.”
    Solution
    Statistics can be used to mislead people.  Ex. the average salary of a University graduating class may be high because of one super rich individual.
  11. Provide two examples of sampling techniques.
    Solution
    ex. Random sampling – anyone
    ex. Stratified sampling – sample people from different types of neighborhoods
    ex. Voluntary sampling – sample people who volunteer to do so
  12. Is the Canadian census mandatory?  What are the pros and cons of this policy?
    Solution
    Yes.  Pro: more accurate information.  Con:  forcing people to do something is pushy
  13. What is the unemployment rate for Canadians?
    Solution
    ≈7%
  14. How does the youth unemployment rate compare?
    Solution
    Approximately twice the national average
  15. What is the U-6 unemployment rate?
    Solution
    The U-6 unemployment rate includes discouraged workers and all other marginally attached workers.  This rate may be almost double the U-3 “official” unemployment rate
  16. What does it mean that the median household income in BC is $70,000?
    Solution
    50% of families make less and 50% of families make more
  17. Floyd Mayweather made $285 million in the year 2018.  If there are 10 boxers at Floyd’s gym, estimate the average salary of each boxer.
    Solution
    $28.5 million (assuming other boxers make $0)
  18. Research a career on using “payscale Canada”.  What is the meaning of the quartile percentages?
    Solution
    Quartile 1 means up to 25% 
    Quartile 2 means up to 50%
    Quartile 3 means up to 75%
    Quartile 4 means up to 100%
  19. How can you succeed in your profession of choice?
    Do what you are good at and enjoy
  20. In Statistics, describe two good sampling principles to improve survey accuracy.
    Solution
    1. Make sure your sample size is not too small
    2. Ask clear questions
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