Data Interpretation Activities
Activity 1
The table below, highlighting the disparity in education attainment by race, is excerpted from the Freedom School Curriculum. By practice, curriculum writers provided relevant documents and data to students to engage them in mathematics inquiry. Freedom School students had stake in understanding how to make sense of the information because it applied to them. To provide historical context for how data analysis was taught to empower the disenfranchised, students will be given time to close-read the data and list what they notice and wonder. The teacher can consider reading the data aloud for students if they find the format confusing and unfamiliar, but the teacher should not explain what the numbers and categories mean until students have adequate time to discuss. The teacher should build on information that students provide and prompt students as necessary.
Table 2. Years of School Completed by Persons 25 or Older, 1960 U.S. Bureau of the Census
Students should consider what data is missing (Information Gap) and reason about what inferences can or cannot be made given the data provided. They may notice the title or named categories and wonder about the overall structure of the table. They may make comparisons within a column, noticing that about 31% of non-white people aged 25 or older completed between 1-4 years of schooling compared to only 5.9% of white people. They will have to interpret what a lower percentage means in this context, considering they may assume a low percentage is unfavorable. They may wonder how to determine the exact number for each category when given the percentage. After collecting and displaying student responses, the teacher will ask students to determine the number of people in each category given the percentage. The teacher will provide calculators and students will work in triads to attempt to determine the number that corresponds to each percentage. The teacher will circulate and offer suggestions only after students attempt and consider whether the number they calculated makes sense in the context of the table. If a student has not inquired, the teacher should ask students to consider how the median information printed below the table is supported by the data in the table. The teacher will prompt the students to find the minimum, maximum, and the lower, upper and inner quartiles of the data. The teacher will ask students to consider whether they have enough data to construct a box plot to show this spread. If they answer no, then they should share what information they believe to be missing (Information Gap).
What can students say about the spread of data? Students should consider how to represent the data visually. Students should notice that the grade ranges are not consistent and should consider how to make equal intervals. How can the data be represented in a more accessible manner? Students may choose to re-create the table with the ranges they select and create a histogram.
Next, students will consider this information in their reality. What could be the consequences of lower education attainment? What might you hypothesize could have an association with the amount of schooling an individual completes? Students will investigate an association between the median salary and years of educational attainment by analyzing data tables from the U.S. Census Bureau.[33] Students will create and interpret scatterplots given the bivariate data. Students will draw a line of best fit, estimate the slope of the line they drew, and write an equation for the line. They should be provided access to graphing calculators or applications such as Desmos to check their work against a computer-generated scatterplot. What do the slope and y-intercept of the line tell us in this context? Students will notice that the y-intercept is a negative number; Does interpreting the y-intercept make sense in this situation? Our first data point is 10 years of education and what happens at 10 years is very different than what happens at 0 years.
Students will make two additional scatterplots from tables that filter for demographics and make observations. For instance, students will make a scatterplot comparing median salary for Black men and years of education and one for another demographic.
Emphasize that correlation is not about determining causation but about looking for trends. Students can compare two variables to see if there is a strong, weak, or no correlation between the variables. In a subsequent activity, students will proceed with graphing residuals and determining the correlation coefficient with technology.
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