# Australian Bureau of Statistics

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 Education Services

 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
• 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.

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
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.

Activity

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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