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MAT 07 – Time Series Data of 15-24 Year Old Road Fatalities


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    Subject Area

    Mathematics


    Suggested Level

    Years 11 - 12


    Overview

    In this activity, students investigate and comment on the changes and trends in road fatality rates for a 10 year period. Optional activities include smoothing and graphing data as well as fitting a linear regression model to make predictions.


    Requirements
  • Access to the internet is desirable
  • Access to CAS calculators or Excel
  • Copy of student worksheet

    Instructions

    Time Series Data of 15-24 year Old Road Fatalities by Sex (Student Worksheet)

    The following table shows the population of 15-24 year olds in Australia.
    1998
    1999
    2000
    2001
    2002
    2003
    2004
    2005
    2006
    2007p
    MALES 15-24 1,330,598 1,326,531 1,333,011 1,351,444 1,373,382 1,397,016 1,420,120 1,446,866 1,474,499 1,499,234
    FEMALES 15-24 1,280,391 1,277,560 1,285,283 1,303,713 1,322,910 1,345,997 1,365,323 1,388,615 1,412,564 1,435,183
    TOTAL 2,610,989 2,604,091 2,618,294 2,655,157 2,696,292 2,743,013 2,785,443 2,835,481 2,887,063 2,934,417

    TABLE 1: Change in the Australian population for 15 – 24 year olds for the period 1998 – 2007. (2007 is a predicted value)
    SOURCE Catalogue no. 3105.0.65.001 Australian Historical Population Statistics, 2008 table 4.1

    Because it has been regularly collected over time the data can be represented in a time series graph where any trend becomes easy to read.



    TASK 1 Population of males and females
    1. Write a sentence describing how the population of 15 – 24 year olds in Australia has changed from 1998 to 2007.

    TASK 2 Road fatalities for males and females
    The following 9 time series graphs have been prepared using the Social Data Set Number S15: Cause of Death by Motor Vehicle Accidents by Sex, 1998-2007 on the Education Services pages of the ABS. Note the rate expressed is per 100,000 in the 15-24 year old age group.




    2. For the time series graph above, write a sentence describing any pattern or trend that is evident and any other points of interest.






    TASK 3 Comparison of road fatalities for males and females by state
    The graphs on the following pages show the rate of fatalities for 15 – 24 year old males and females by State and Territory.


















    NOTE Data for females in 2000 and 2005 not published



    NOTE Data for females in 1999, 2001, 2004 and 2005 not published



    NOTE Data for males in 2001, 2003 and 2004 and females 1998     - 2004 not published

    3. Comment on any similarities and differences in the State and Territory graphs compared with the graph of Australia. Give possible reasons to explain your observations.

    4. Select a State or Territory of interest to you. Comment on whether the rate of death is higher or lower than the National rate. Comment on any reasons there may be for this. Note insufficient information may be provided in the NT, SA and ACT graphs to complete a full comparison.


    5. Use the population figures in Table 2 to calculate an estimate of the actual number of deaths in 1998 and 2007 for your chosen State or Territory for this age group. Show your answers in Table 3 and include examples of your working out. Note your results will be more accurate if you use the actual numbers in the S15 data set rather than reading the time series graphs. Discuss how the number of actual deaths has changed in this time.


    males
    females
    1998
    2007
    		diff
    1998
    2007
    		diff
    NSW 440,427 485,819 45,392 423,698 463,730 40,032
    VIC 325,048 377,960 52,912 315,097 357,570 42,473
    QLD 253,958 303,954 49,996 245,983 292,343 46,360
    SA 101,035 110,956 9,921 96,391 105,474 9,083
    WA 134,986 157,825 22,839 128,147 146,614 18,467
    Tas 32,527 33,207 680 31,400 31,876 476
    NT 16,260 17,387 1,127 14,719 16,135 1,416
    ACT 26,204 28,259 2,055 24,846 26,542 1,696
    Table 2 Population by State and Sex 1998 and 2007 (Catalogue no. 3201.0)

    males
    females
    1998
    2007
    diff
    1998
    2007
    diff
    NSW
    VIC
    QLD
    SA
    WA
    Tas
    NT
    ACT
    Table 3: Estimated number of actual road fatalities 15 - 24 per State 1998 and 2007



    Optional Questions
    TASK 4 Smoothing the Data
    For your selected State or Territory,
    a) Use an appropriate method to smooth the data and graph the smoothed data.
    b) Fit a linear regression line (trend line) and interpret the equation in terms of the variables.
    c) Interpret the slope and y intercept of the regression line.
    d) Use the equation of the regression line to predict both the rate of deaths for 2005 and 2010.
    e) Comment on the accuracy of the regression line for making predictions.
    f) Comment on how you could attempt to improve the reliability of your predictions for your chosen State or Territory.

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    Solution

To provide any feedback regarding this activity, please contact ABS Education Services on 1800 623 273 or email education@abs.gov.au.

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