Social Justice Mathematics Project 3: "Median Household Incomes Over Time"
Overview
In this project students will explore changes in income over time for the three largest racial/ethnic groups: Whites, Blacks and Hispanics.
Students Will:
- Graph real data income data from different ethnic groups over time.
- Make decisions about which data set is best for comparison.
- Graph differences in income between ethnic groups.
- Compute the differences in income for each of the groups
- Draw conclusions about the characteristics of the graphs and the average rate of change.
- General Education (Quantitative Reasoning)
Social Justice Mathematics "Median Household Incomes by Ethnicity: Exploring Data"
The following data from the US Census Bureau [1] gives the the median incomes of three largest racial groups in the US. You will use this data to evaluate disparities between whites and Blacks/Hispanics in household income.
| White Alone not Hispanic | Black Alone | Hispanic any race
| ||||||
Year | Number (thousands) | Median income | Number (thousands) | Median income | Number (thousands) | Median income | |||
Current | 2020 | Current | 2020 | Current | 2020 | ||||
2020 | 85,336 | 74,912 | 74,912 | 17,358 | 45,870 | 45,870 | 18,349 | 55,321 | 55,321 |
2019 | 84,868 | 76,057 | 77,007 | 17,054 | 45,438 | 46,005 | 17,667 | 56,113 | 56,814 |
2018 | 84,727 | 70,642 | 72,820 | 17,167 | 41,361 | 42,636 | 17,758 | 51,450 | 53,036 |
2017 (40) | 84,706 | 68,189 | 72,005 | 17,019 | 39,365 | 41,568 | 17,336 | 50,167 | 52,974 |
2017 | 84,681 | 68,145 | 71,958 | 16,997 | 40,258 | 42,511 | 17,318 | 50,486 | 53,311 |
2016 | 84,387 | 65,041 | 70,157 | 16,733 | 39,490 | 42,596 | 16,915 | 47,675 | 51,425 |
2015 | 84,445 | 62,950 | 68,778 | 16,539 | 36,898 | 40,314 | 16,667 | 45,148 | 49,328 |
2014 | 84,228 | 60,256 | 65,948 | 16,437 | 35,398 | 38,742 | 16,239 | 42,491 | 46,505 |
2013 (39) | 84,432 | 60,329 | 67,146 | 16,009 | 35,324 | 39,315 | 16,088 | 39,687 | 44,171 |
2013 (38) | 83,641 | 58,270 | 64,854 | 16,108 | 34,598 | 38,507 | 15,811 | 40,963 | 45,592 |
2012 | 83,792 | 57,009 | 64,391 | 15,872 | 33,321 | 37,635 | 15,589 | 39,005 | 44,055 |
2011 | 83,573 | 55,412 | 63,912 | 15,583 | 32,229 | 37,173 | 14,939 | 38,624 | 44,549 |
2010 (37) | 83,314 | 54,460 | 64,794 | 15,265 | 32,124 | 38,220 | 14,435 | 37,631 | 44,772 |
2009 (36) | 83,158 | 54,461 | 65,865 | 14,730 | 32,584 | 39,407 | 13,298 | 38,039 | 46,004 |
2008 | 82,884 | 55,530 | 66,924 | 14,595 | 34,218 | 41,239 | 13,425 | 37,913 | 45,692 |
2007 | 82,765 | 54,920 | 68,731 | 14,551 | 33,916 | 42,445 | 13,339 | 38,679 | 48,406 |
2006 | 82,675 | 52,423 | 67,467 | 14,354 | 31,969 | 41,143 | 12,973 | 37,781 | 48,623 |
2005 | 82,003 | 50,784 | 67,476 | 14,002 | 30,858 | 41,001 | 12,519 | 35,967 | 47,789 |
2004 (35) | 81,628 | 48,910 | 67,187 | 13,809 | 30,095 | 41,341 | 12,178 | 34,271 | 47,078 |
2003 | 81,148 | 47,777 | 67,404 | 13,629 | 29,645 | 41,823 | 11,693 | 32,997 | 46,552 |
2002 | 81,166 | 46,900 | 67,669 | 13,465 | 29,026 | 41,880 | 11,339 | 33,103 | 47,763 |
[1] US Census Bureau (2022) Table H-5. Race and Hispanic Origin of Householder -- Households by Median and Mean Income
Social Justice Mathematics Project "Median Household Incomes by Ethnicity: Working with Data"
Compare the following data to the data in the previous page. Explain why the values for median and mean are different? How is each computed and why in the case of income does the data appear to be so different? Make up or find smaller data sets that illustrate how differences in median and mean can vary.
| White Alone not Hispanic | Black Alone | Hispanic Any Race | |||
Year | Mean income | Mean income | Mean income | |||
Current | 2020 | Current | 2020 | Current | 2020 | |
2020 | 104,754 | 104,754 | 67,593 | 67,593 | 75,193 | 75,193 |
2019 | 106,659 | 107,990 | 66,553 | 67,384 | 75,058 | 75,995 |
2018 | 98,261 | 101,290 | 58,665 | 60,473 | 70,945 | 73,132 |
2017 (40) | 95,759 | 101,117 | 58,029 | 61,276 | 67,663 | 71,449 |
2017 | 93,453 | 98,682 | 58,593 | 61,872 | 68,319 | 72,142 |
2016 | 89,757 | 96,818 | 57,445 | 61,964 | 66,815 | 72,071 |
2015 | 85,585 | 93,508 | 54,352 | 59,384 | 63,612 | 69,501 |
2014 | 82,465 | 90,255 | 51,230 | 56,069 | 57,534 | 62,969 |
2013 (39) | 81,228 | 90,406 | 50,454 | 56,155 | 57,617 | 64,127 |
2013 (38) | 79,340 | 88,305 | 49,629 | 55,237 | 54,644 | 60,818 |
2012 | 77,843 | 87,922 | 47,737 | 53,918 | 53,422 | 60,339 |
2011 | 76,063 | 87,731 | 47,255 | 54,504 | 52,352 | 60,383 |
2010 (37) | 73,333 | 87,249 | 44,957 | 53,488 | 51,394 | 61,147 |
2009 (36) | 73,240 | 88,576 | 46,046 | 55,688 | 52,229 | 63,165 |
2008 | 74,102 | 89,307 | 46,533 | 56,081 | 51,572 | 62,154 |
2007 | 73,182 | 91,586 | 46,631 | 58,358 | 50,828 | 63,610 |
2006 | 71,745 | 92,334 | 45,127 | 58,077 | 50,575 | 65,088 |
2005 | 68,603 | 91,152 | 42,454 | 56,408 | 47,138 | 62,632 |
2004 (35) | 65,258 | 89,645 | 40,633 | 55,817 | 45,877 | 63,021 |
2003 | 63,887 | 90,132 | 40,131 | 56,617 | 44,468 | 62,736 |
2002 | 62,115 | 89,622 | 40,011 | 57,730 | 44,887 | 64,765 |
Social Justice Mathematics "Median Household Incomes by Ethnicity: Plotting the Data"
You will be analyzing a data set provided by the US Census bureau about changes in median income for three ethnic groups (White, Hispanic, Black). You will be utilizing your TI-84 Calculator to graph the data. You must answer each of the following questions.
1. Graph the year vs. ethnic group data. In the TI calculator, you can create three graphs in which L1 represents the year. In each of the three graphs L2, L3, and L4 will represent the income for each ethnic group. Also, if you are using the TI calculator, only use 5 rows of data that are about equally spaced. If you are using your calculator you must take a picture of your graph and include it in you submission document. If you are using EXCEL, you will use the scatter plot function. Use all the data if you are using EXCEL. (5 pts)
2. Graph the year vs. Gap Between White and Hispanic Incomes and Year vs. Gap Between White and Black Incomes on separate graphs (Hint: You must first compute the Gap Between White and Hispanic Incomes by taking L2 - L3 in L5, and then compute the Gap Between White and Hispanic Incomes by taking L2-L4 in L6). Also, if you are using the TI calculator, only use 5 rows of data that are about equally spaced Again, if you are using EXCEL, you will use the scatter plot function, and use all the years. (5 pts)
Social Justice Mathematics Project "Median Household Incomes by Ethnicity: Analyzing data and drawing conclusions"
1. Describe any trends that you observe regarding the first graph of data such as:
- Is one group's data set consistently higher than the other? (1 pt)
- Does the data for each graph generally trend up, down, or is there some other pattern? (1 pt)
- Do you know the names of any curves that might be good at estimating/following the points? (1 pt)
2. Describe any trends that you observe regarding the graph of household income gap data such as:
- Do the income differences (between Whites and Hispanics and between Whites and Blacks) generally follow identical patterns or do they diverge significantly? (1 pt)
- Are there years when the income differences drop or widen significantly? (1 pt)
- Would it be fair to use linear equations to model the gap differences or is there some other curve that makes more sense? (1 pt)
- What data is missing from the data sets that might be important to consider? (1 pt)
3. Explain each of the following:
- Why do you think the differences persist over time? (2 pts)
- What do you think may be the causes for significant increases/decreases in gaps between Whites and other ethnic groups during some years? (2 pts)
- What are ways that you can think of to decrease gaps between Whites and other ethnic groups? (2 pts)
- Are some gaps in income acceptable? Why or why not? (2 pts)