Function modelling using secondary data from E-STAT

In the real world, graphs related to human population or socioeconomic statistics rarely approximate any mathematical functions other than linear functions. However, there are some occasions where the underlying conditions lead to trends that closely approximate quadratic, exponential, sinusoidal and logistic functions or combinations of these functions.

Provided below are examples where real world data from Statistics Canada surveys can be approximated by function models. All data are extracted from E-STAT, a database available to registered educational institutions.

You can access E-STAT temporarily by using:

Read the E-STAT licence before using this password.

Note: You must use this information for educational purposes only.

• Extracting data from E-STAT
• Suggestions for classroom use
• What teachers are saying

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Linear

Click on graph to see more examples.

Topic	Years	Table number	Vector number
Total population	1971 to 2005	051-0001	v466668
Median age	1971 to 2005	051-0001	v466689
Revenue of fitness centres	2000 to 2004	361-0002	v1885072
Energy use by the business sector	1993 to 2000	153-0032	v29505744
Total pregnancies	1992 to 2000	106-9002	v14225258
Enterprises with a website	2000 to 2005	358-0008	v2651352
Life expectancy	1979 to 1999	102-0025	v5939197
Bottled water	1995 to 2001	002-0011	v783736
Lung cancer incidence (women)	1976 to 2004	103-0204	v41338730
Military personnel **Piecewise Linear**	1969 to 1998	183-0004	v130106

• Lesson plan: Linear modelling of the life expectancy of Canadians (view)

 

Quadratic

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Topic	Years	Table number	Vector number
Canadian births **Convert to "Annual (sum)" under Manipulate data**	1948 to 1968	053-0001	v62
Number of males registered in apprenticeship programs	1991 to 2001	477-0051	v21691205
Lung cancer incidence (males)	1976 to 2000	103-0204	v41338718
Birth rate for women 40 years and over	1974 to 1999	106-9002	v14225341
Number of homicides by shooting	1978 to 1982	253-0002	v1489239

• Lesson plan: Quadratic modelling of Canada's Baby Boom (view)
• Lesson plan: Quadratic modelling of the number of males registered in apprenticeship programs (view)

 

Exponential

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Topic	Years	Table number	Vector number
Federal debt	1955 to 1997	385-0010	v151537
Consumer price index	1951 to 2005	326-0002	v737344
Farm value of potatoes	1908 to 2004	001-0014	v47184
Infant mortality rate	1979 to 2005	102-0030	v5939543
Households with air conditioning	1999 to 2006	203-0020	v28469581
Urban population	1871 to 1971	075-0010	v742085

• Lesson plan: Exponential modelling of the farm value of potatoes (view)

 

Sinusoidal

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Topic	Years	Table number	Vector number
Population aged 20-24	1971 to 2005	051-0001	v466758
Employment in the public sector **Convert to "Annual (average)" under Manipulate data**	1981 to 2005	183-0002	v135015
Production of beer	2000 to 2003	303-0019	v1552
Imports of fresh fruits and berries	2000 to 2004	226-0002	v212580
Induced abortions for women under 20 years of age	1974 to 2003	106-9034	v31232487
International travellers to Canada (inbound)	1999 to 2008	387-0004	v81688
Employment rate	2002 to 2008	282-0001	v2091219

• Lesson plan: Sinusoidal modelling of Canada's youth cohorts (view)

 

Logistic

Click on graph to enlarge.

Topic	Years	Table number	Vector number
Cable television industry revenues	1976 to 2000	353-0001	v81330
Movie theatre ticket prices	1996 to 2005	501-0010	v26563414

 

Combined

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Topic	Years	Table number	Vector number
Canadian births ** Quadratic + Sinusoidal **	1955 to 1965	053-0001	v62
International travellers to Canada (inbound) ** Linear + Sinusoidal **	1999 to 2007	387-0004	v81688
Imports of fresh fruits and berries ** Linear + Sinusoidal **	1980 to 2004	226-0002	v212580
Employment rate ** Linear + Sinusoidal **	1993 to 2008	282-0001	v2091219
Urban and rural population ** Linear + Exponential **	1871 to 1971	075-0010	v742084

 

Extracting data from E-STAT

1. You have two options:
   • To retrieve the pre-selected variable choices, click on the Vector number.
   • To select alternatives for the variables, click on the Table number.
2. The next steps differ depending on your selection in #1:
   • If you selected the Vector number, click on the Continue button.
   • If you selected the Table number, select value(s) of interest for each dimension of the table and then click on the Retrieve as individual Time Series button.
3. On the Output specification page, select the type of graph or table you wish to have displayed and then click on the Retrieve now button. Ensure that the start and end dates for the dataset are correct.
   • If you wish to display a graph within E-STAT, select one of the graph types and click on the Retrieve now button. We recommend these types: Line graph, Line graph with symbols and Scatter graph.
   • If you wish to use the data in a dynamic statistical software program (e.g., Fathom), select Plain text: Table, time as rows and then click on the Retrieve now button. Highlight only the numeric data (not the legend, headings, footnotes, or references), select Copy, and then Paste in your software program.
   • If you wish to use the data in a spreadsheet software program (e.g., Excel), select CSV (comma-separated values) file: Time as rows and then click on the Retrieve now button.

Suggestions for classroom use

1. Have students research the reasons (historical, social, economic, etc.) why certain data follow certain patterns. 
   Suggestions:
   • See footnotes attached to the tables for more information.
   • See The Daily attached to the tables for a summary of data trends which is linked directly under the table name as "View latest article from The Daily related to this table".
2. Have students import the data into a data analysis program and fit a function to the data by altering variable values.
3. As a summative assessment of your course or unit on mathematical functions, give the students one of the real-world datasets above. Ask them to demonstrate their understanding of the course or unit by preparing a written analysis of this dataset. Evaluate the students' mathematical analysis and communication skills.