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Part (a) Write an appropriate survey question

Most students were able to write a reasonable survey question in part (a), but some questions were incomplete or vague. The following two responses were considered to be incomplete as they do not make it clear that the question is asking about day of the week for a family statistics event, and these two responses were scored as only partially correct for part (a).

The following three student responses illustrate responses that were scored as partially correct because they are questions that are ambiguous or not clearly worded.

The following student response was also considered to be only partially correct for part (a)—notice that for this student, a “family statistics event” is a statistics test!

Another student error in answering part (a) is illustrated in the following two student responses. In these responses, the student does not actually provide a question that could be used in to survey students at the school.

The final student error observed in responses to part (a) was providing a question that would not result in appropriate data. For example, consider the following student response, which would not provide data on preferred day of the week.

Part (b) Demonstrate an understanding of anticipated variability in responses to a survey question

There were several common student errors in constructing the table requested in part (b). The most concerning error was failure to provide realistic counts that appropriately acknowledge anticipated variability in the responses to the survey question. This represents a conceptual misunderstanding regarding the nature of data. This is illustrated in the following two student responses to part (b). These responses were viewed as unrealistic in that the counts given for each possible response are unlikely to be identical when data is collected from 1000 students. These two responses were considered to be only partially correct for part (b).

Two additional examples of student responses for which the given table and counts were considered unrealistic are provided by the following student responses. In the first example, only Friday and Wednesday are given as possible responses. In the second example, in addition to having equal counts specified for each possible response, the counts are not integers.

Another common error in answering part (b) is illustrated in the following three student responses. These responses provided graphs or pictographs in part (b) even though the question asked for a table.

Some students did not provide complete tables in their responses to part (b), either giving just the possible responses with no associated counts or giving counts without listing the possible responses to the survey question. This error is illustrated by the following three student responses which were scored as incorrect for part (b).

Part (c) Create an appropriate graphical display

There were several common student errors in constructing a graphical display in part (c). 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. Both of these responses do not have a label for the vertical axis and were considered to be only partially correct for part (c).

Some students constructed a graphical display that was appropriate for categorical data, but which was not correct for the data given in their answer to part (b) of this question. For example, the following student response to part (c) included categories that were not part of this student’s answer to part (b) (Next Mon, Next Tues) and the heights of the bars did not correspond to the counts given in the student’s part (b) answer.

A surprising number of students attempted to construct graphical displays that were not appropriate for categorical data. Two examples of student responses that illustrate this error and that were scored as incorrect for part (c) follow.

There was also one other common error that was considered minor. While this error did not impact the score on part (c), it is worth mentioning because it occurred often. When constructing a bar graph, many students ran all of the bars in the bar graph together. In constructing a bar graph for the categorical data, the bars that represent categories in a bar graph should be separated (as in the response shown below). While this error (illustrated in the second response below) was considered a minor error and responses making this mistake still received a score of essentially correct for part (c), such responses would have been stronger if the bar graph had been correctly drawn.

Correct Bar Graph (bars separated)

Incorrect Bar Graph (bars run together)