Student instructions
Sinusoidal modelling of Canada's youth cohorts

Background information

A graph of data based on human activities rarely approximates the shape of a sine curve with any accuracy. However, occasionally the underlying conditions lead to trends that closely follow a sinusoidal curve. The Baby Boom occurred after World War II, when Canadian soldiers returned and started having children in record numbers. As such, there was a great increase in the number of births beginning in 1946, the first year after World War II ended. Births increased for several years and then began to decline. As a result of the Baby Boom, distributions of certain age cohorts in Canada closely approximate a sine curve.

In this activity, you will obtain data on the number of 20 to 24 year-olds in Canada from the E-STAT database on the Statistics Canada website. You will import these data into a statistical software program in order to approximate the parametric form of a sine curve [y = a sin(k(x – d)) + c] to these data by varying the parameter values (a, k, d, and c).

E-STAT instructions

1. Go to the E-STAT website.
2. Select English.
3. Click on Table of contents on the left sidebar.
4. Under People, select Population and demography.
5. Under CANSIM, select Population estimates and projections.
6. Select Table 051-0001 – Estimates of population, by age group and sex for July 1, Canada, provinces and territories, annual (persons).
7. On the Subset selection page:
   • Select Canada
   • Select Both sexes
   • Select 20 to 24 years
   • Under From, select 1971
   • Under To, select 2006
8. Click on the Retrieve as individual Time Series button.
9. 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.
10. Click on the Retrieve now button.

Generic statistical software instructions

Note: Specific instructions for dynamic statistical software (PDF, 71 Kb) (e.g., Fathom) are also provided.

1. Import your data into your statistical software program.
2. Save your file as Youth cohorts.
3. Create a new attribute, Years since 1971, using the following formula:
   Years since 1971 = Year – 1971
4. Create a scatter plot with Years since 1971 on the x-axis and Population aged 20 to 24 on the y-axis.
5. Plot the following function on your scatter plot:
   
   Note: It is necessary to use instead of just k in this equation because the variable on the x-axis is measured in non-angle units (the number of years since 1971) as opposed to angle units (radians).
6. Alter the values of a, k, d, and c until your function closely approximates the data in the scatter plot.

***** Go to your worksheet and answer questions #1 to 8. *****