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Web Activities
CHAPTER 4 QUADRATIC AND RECIPROCAL FUNCTIONS
The Scenario
Every 5 years , the Federal Government of Canada conducts a census. Information
from the census is used to analyze trends in the Canadian population.
The categories of data collected include population, education, labour,
families & households, income, housing, and household activities.
In this activity, you'll focus on two facets of the income data collected.
How does the average income of Canadian male citizens vary with age?
Does the average income of Canadian female citizens vary with age in a
similar manner as that of the male population?
Investigating Temperature Functions
- Use the data from the 1996 census to investigate the average income
of Canadians. completing a table like the one below. (For the purposes
of modelling use the mean age in each range.)
| MEAN AGE |
AVERAGE
INCOME
— MALE ($) |
AVERAGE INCOME
— FEMALE ($) |
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- Using the same graph, create a scatter plot for both genders
using mean age as the independent variable and average income
as the dependent variable. Draw the curve of best fit for each
situation.
- Using the graphs you created predict the age at which the average
income for males and females is at its maximum.
- Use quadratic regression and the TI-83 plus calculator to determine
the equation of both curves of best fit. Round off all values
to the nearest hundredth.
- Complete the square of both regression equations to determine
the maximum average incomes and the ages at which they occur.
Verify your results using the maximum operation on the CALC menu.
Your Job
Create a report that includes the following items:
- a table of the data you collected , the corresponding scatter
plots you created including the curves of best fit.
- your predictions of the ages at which average income is at a
maximum for both males and females based on your graphs.
- the equations of the algebraic models you determined through
quadratic regression.
- the calculations you used to complete the square of both regression
equations and the maximum values that they provide.
- a paragraph that provides some possible reasons why the data
behaves the way it does.
- a paragraph that compares and contrasts the male and female
data that includes some possible reasons for the differences in
the data.
Your report must be at least 500 words (approximately two
double-spaced pages). You will be assessed on how well the report
addresses the criteria mentioned above.
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