Student instructions
Quadratic modelling of Canada's Baby Boom

Background information

A graph of the human population rarely approximates the shape of a parabola with any accuracy. However, underlying conditions occasionally lead to population trends that closely follow a parabolic shape over specific time periods. The Baby Boom occurred right after World War II. Canadian soldiers returning in great numbers after the war started having children within a few years after returning to Canada, which resulted in a huge increase in the number of births. The number of births increased for several years and then began to decline. In this activity, you will determine if a parabola can be a useful model for the number of births per year for this post-war Baby Boom period.

E-STAT instructions

1. Go to the E-STAT website.
2. Select English.
3. Click on Search CANSIM on the left sidebar.
4. Type 053-0001 in the Search box and click on the Search button to retrieve Table 053-0001 – Vital statistics, births, deaths and marriages, quarterly (number).
5. On the Subset selection page:
   • Under Geography, select Canada
   • Under Estimates, select Births
   • Under From, select Jan 1950
   • Under To, select Dec 1968
6. Click on the Retrieve as individual Time Series button.
7. On the Output specification page, select either "Plain text: Table, time as rows", "HTML, table: Time as rows" or "CSV: Time as rows". The output selected will depend on your software. Ask your teacher which format works best with your school's software.
8. Click on the Manipulate data button at the bottom of the screen.
9. Under Frequency of output data will be:, then under Converted to:, select Annual (sum).
   The data as retrieved were quarterly (every three months). By selecting Annual (sum), you are adding the quarterly data together to result in an annual total.
10. Click on the Retrieve now button.

Generic statistical software instructions

Note: Specific instructions for Dynamic statistical software (PDF, 45 Kb) (e.g. Fathom) are also provided.

1. Import your data into your statistical software program.
2. Save your file as Baby Boom.
3. Create a scatter plot with Year on the x-axis and Number of births on the y-axis.
4. Plot the following function on your scatter plot:
   Number of births = a(Year – h)² + k

   ***** Go to your worksheet and answer questions #1 to 11. *****

5. Alter the values of a, h, and k until your function closely approximates the data in the scatter plot.

   ***** Go to your worksheet and answer questions #12 to 18. *****