2.3: Measuring Population Change

INTRODUCTION

The table below shows the apportionment of representatives (seats) after the 2020 census. Make note of the table legend and the colors used for the states, discuss with your group the questions below.

• Which states have the largest populations?
• Which states have small populations?
• Which states are growing fastest and growing slowest?
• What does it mean to be growing fastest in terms of representation?

SPECIFIC OBJECTIVES

By the end of this collaboration, you should understand that

• a relative change is different from an absolute change.
• a relative measure is always a comparison of two numbers.

By the end of this collaboration, you should be able to

• calculate a relative change.
• explain the difference between relative change and absolute change.

PROBLEM SITUATION: HOW THE CENSUS AFFECTS THE HOUSE OF REPRESENTATIVES

Every 10 years, the United States conducts a census. The census tells us how many people live in each state. You can also find out how much populations have changed over time from the census data. The original purpose of the census was to decide on the number of representatives each state would have in the House of Representatives. Census data continue to be used for this purpose, but now there are many other uses for the data. For example, governments may use the data to plan for public services such as fire stations and schools.

In this problem situation, your instructor will ask your team to explore data from one of two census regions: 1) South Atlantic States or 2) Mountain States. There are tables on the next page that show the population of each state in these census regions in 2010 and 2020. You will be asked to calculate the population growth (in people) as a percentage for each state in your assigned region, and for the region as a whole. You will examine how this affects the number of representatives each state has in the House of Representatives.

The absolute change in a state’s population tells us by how many people the population has changed. The relative change is the change as it compares to the earlier population. Often relative change is given as a percentage. See the table below for an example using the population change in California from 2010 to 2020.

Use the following data to answer Questions 1–6.

South Atlantic States

Mountain States

(1) Calculate the absolute change in the population of each state. Write your answers in the appropriate table.

(2) Calculate the relative change in the population of each state. Write your answers in percent form in the table above.

(3) List the state in each region that changed the most in absolute population.

(4) List the state in each region that had the largest relative increase in population.

(5) Explain why the lists in Question 3 and Question 4 are not the same.

(6) Use the previous information to calculate the following absolute and relative changes in total population. Do the calculations on your own first before sharing in your group.

(a) The absolute change in total population for the three Mountain Region states.

(b) The relative change in total population for the three Mountain Region states.

(c) The absolute change in total population for the three South Atlantic Region states.

(d) The relative change in total population for the three South Atlantic Region states.

(7) Let’s now consider a state we have not explored yet: Illinois. Interestingly, the population of the state of Illinois actually decreased between 2010 and 2020. Illinois had a population of 12,864,380 in 2010. Its population was 12,822,739 in 2020.

(a) What was the absolute change in Illinois’ population?

(b) What was the relative change in Illinois’ population? Write a statement that describes the relative change in Illinois’ population between 2010 and 2020. Think about this on your own first before sharing with your group. Round your answer to the nearest hundredth of a percent.

FURTHER APPLICATIONS

(8) In 2019, the U.S. Congress debated cutting the federal budget. The goal was to reduce the national debt, which was $23 trillion.

(a) If one group wanted to reduce the budget by $500 billion. How large is this change relative to the national debt?

(b) If another group wanted to reduce the budget by $200 billion. How large is this change relative to the national debt?

(c) If a politician wanted to argue for the larger cut, do you think the politician should use the absolute or the relative change to justify his or her position? Why?

(d) If a politician wanted to argue for the smaller cut, do you think the politician should use the absolute or the relative change to justify his or her positions? Why?

MAKING CONNECTIONS

Record the important mathematical ideas from the discussion.