A student constructed a graph to show how many of a town\'s residents have compl

Question

A student constructed a graph to show how many of a town's residents have completed five different levels of education (elementary school, high school, two years of college, four years of college, graduate school). Which student explanation shows correct mathematical thinking? "I used a histogram, because the levels of education are consecutive intervals on a number scale." "I used bar graph because it compares the number of people in each level of education." "l used a line graph because it shows how the level of education changes over time." "I used a scatter plot because it compares the number of people with their level of education."

Explanation / Answer

Histograms are used to show distributions of variables while bar charts are used to compare variables. Bar graphs are used to compare things between different groups or to track changes over time. Line graphs are used to track changes over certain periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Scatterplots are used to determine relationships between the two different variables. The x-axis is used to measure one variable and the y-axis is used to measure the other. In the present case,the graph has to depict the number of a town’s residents who have completed five different levels of education i.e. elementary school, high school, two years of college, four years of college, and graduate scool. A person who has completed graduate scool has also completed the other 4 levels of education, a person who has completed 4 years of college has completed the other 3 levels of education that come before it and so on. In these circumstances, a bar graph is the most appropriate graph to use. The bars would represent the number of people who have completed 1,2,3, 4 or 5 levels of education. The height of the bars would keep declining with increasing numbers of level of education. It would be the best depiction of the given scenario. The 2nd option is the correct answer.

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