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Part (a) Create an appropriate graphical display

There were several common student errors in constructing a graphical display in part (a). By far the most common error was to omit scales or labels on the axes of chosen graphical display. The following two student responses illustrate this error. In the first response, neither axis in the scatterplot is labeled, while in the second response the age axis is not labeled and there is no vertical scale or label given. Both of these responses are considered to be only partially correct for part (a).

Some students constructed graphical displays that did not use age on one of the axes, or constructed other types of displays that do not facilitate comparison of the two groups across the ages. Two examples of student responses that illustrate this error and that were scored as incorrect for part (a) follow.

There were also two errors that were considered minor. While these errors did not impact the score on part (a), they are worth mentioning because they occurred often. Both of these errors occurred in responses that used the comparative bar chart. The first of these errors was not starting the vertical axis at 0. While it is not uncommon for axes in a scatterplot to not cross at (0,0), in bar charts or histograms, the vertical axis should always start at 0. Starting the axis at something other than 0 distorts comparisons and can make differences between groups look larger. The following student response shows a break in the vertical axis. While this response was still considered as essentially correct for part (a), the response would have been stronger if the vertical axis had been constructed correctly.

Another common error was to run all the bars in the bar graph together. In constructing a bar graph for the given data, age is considered as an age group category, and the bars that represent categories in a bar graph are separated (as in the response shown above). The following response illustrates this error. Again, this was considered a minor error and this response still received a score of essentially correct for part (a), but the response would have been stronger if the bar graph had been correctly drawn.

Parts (b) and (c)  Use information from a graphical display to compare two groups

In parts (b) and (c) there were three common errors: (1) failure to make a statement that addressed the “across the different age groups” aspect of the problem; (2) failure to make a statement that addressed both groups; and (3) providing a weak description/justification of the similarity (part (b)) or difference (part (c)).

The following student responses were all scored as incorrect for part (b) or part (c) because they do not provide a statement that acknowledges a similarity or difference across the ages.

Some responses made general statements that failed to reference both groups. This is illustrated in the following responses to part (b), which were scored as partially correct. If these responses had indicated that the statement was true for both groups, they would have received a higher score for part (b).

The third common error in parts (b) and (c) was to provide a weak explanation or justification. This is illustrated in the following student responses, which were scored as partially correct. These responses would be stronger if they had been more specific and descriptive and referenced both age and percent ownership as well as the two groups.

There was one other error on parts (b) and (c) that also occurred, although less frequently than the other errors mentioned here. These responses focused on the different group sizes (district versus nation) in the response. Such responses were scored as incorrect because they did not address the question asked. The following student response illustrates this, and is typical of those making this error.