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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
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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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|
|
|
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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.
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Using the graphs you created predict the age at which
the average income for males and females is at its maximum.
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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.
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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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