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Part (a) Construct a dot plot

Responses that were not scored as essentially correct for part (a) generally made one of four common mistakes. A few students knew how to construct a dot plot, but misplaced one of more of the dots. This is illustrated in the following student response in which the three dots corresponding to teams with 4 letter names have been shown above 5 rather than correctly placed at 4. This response was scored as partially correct for part (a).

By far the most common error was made by students who did not take the time to understand the data that presented in the given table. These students took the values in the second column of the table as the complete data set. They did not realize that there were three teams whose names contain 4 letters, three teams whose names contained 6 letters, and so on. This resulted in dot plots like the one in the following student response. Because students producing a dot plot like this one show an understanding of what a dot plot is and how to construct a dot plot, these dot plots were scored as partially correct for part (a).

Other students did not read the question carefully and so did not realize it was asking for a dot plot of the data for the National League teams. These students just reproduced the given American League team name length dot plot. The following student response provides an example of this error.

Finally, a number of students did not seem to know what a dot plot was and did not realize that they could model their plot on the dot plot for American League teams that was provided. These students produced incorrect graphs. In the following student response, the student recognizes that there are name lengths of 4, 6, 7, 8, 9 and 12 but then constructed a plot by putting 4 dots at 4, 6 dots at 6, 7 dots at 7, and so on. This response was scored as incorrect for part (a).

The following three student responses were also scored as incorrect for part (a), because the display constructed is not a dot plot. Students who constructed displays such as these then had a difficult time answering part (b) because it made it difficult to compare the length distributions for the two leagues.

Parts (b) Recognize that data distributions that are centered in about the same place might still differ in variability or shape

Part (b) asks students to compare two distributions. The most common errors in part (b) are the result of focusing on individual values in each data set rather than considering the distribution as a whole. For example, in the following response, the student focuses on one data value in the American League distribution (5 letters) and points out that there is no team in the National League with a name that has exactly 5 letters. This student is not considering differences in the distributions.

Other students focused only on the outlier in the National League data set. Again these students are not thinking about the distributions as a whole. This is illustrated in the following two student responses.

Students who produced an incorrect dot plot in part (a) often had difficulty in answering part (b). In the student response below, because the dot plot was not constructed in a way that showed multiple teams with the same length names, the student incorrectly concludes that the difference between the American League team name lengths and the National League team name lengths is that the American League had some teams that had the same number of letters in their names.

Even though the questions stated that the mean and median team name lengths for the two leagues were “about” the same, some students chose to focus on the fact that the means or medians were not exactly equal. This is illustrated in the following two student responses, which were scored as incorrect as they did not consider other characteristics of the distributions, such as spread or shape.