Assessing Students' Understanding of Variability in Graphical Representations that Share the Common Attribute of Bars

Figures & data

Figure 1. Visual aids to view variability in graphical representations of quantitative data (Cooper and Shore 2010).

Table 1. Distribution of subjects by major and prior experience with statistics.

Major	Prior statistics course	No prior statistics course	Total
Math secondary education	5	4	9
Computer science/economics	9	5	14
Total	14	9	23

Figure 2. Distribution of the number of correct responses on part I among all students.

Figure 3. Distribution of the number of correct responses on part I by prior statistics course.

Table 2. Number of correct responses (out of 7) on part I by prior statistics course.

	n	Median	Mean	St. dev.
Students with no prior statistics course	9	2.0	2.8	1.6
Students who had a prior statistics course	14	3.5	3.5	1.2
Combined	23	3.0	3.2	1.3

Figure 4. Assessment item 1—histogram.

Figure 5. Assessment item 5—histogram.

Figure 6. Assessment item 2—bar graph.

Figure 7. Assessment item 4—bar graph.

Figure 8. Assessment item 3—value bar chart.

Figure 9. Assessment item 6—value bar chart.

Figure 10. Student thinking about variability transferred across graph types.

Figure 11. Assessment items 7, 8, and 9.

Figure 12. Reference for the terms distribution, data values, and variable.

Table 3. A summary of students' visual (mis)interpretations of variability by graph type.

Prominent visual	Graph type
interpretations of variability	Value bar chart	Bar graph	Histogram
Level Bars indicate greatest variability of the data	Incorrect interpretation -Cases on the horizontal axis are being treated as if they were [categorical] data with values on the vertical axis perceived to indicate the distribution of data.	Correct Interpretation	Incorrect Interpretation -The data is being treated as if it were categorical. The more unalike the data values, the greater the variability.
Large Variability of Bar Heights indicates large variability of data	Correct Interpretation	Incorrect Interpretation -Bar heights are perceived to be the data values.	Incorrect Interpretation -Bar heights are perceived to be the data values.

——— (2010), “The Effects of Data and Graph Type on Concepts and Visualizations of Variability,” Journal of Statistics Education, 18, 1–16. Available at http://www.amstat.org/publications/jse/v18n2/cooper.pdf

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