Getting Started 
Misconception/Error The student does not select a measure of center based on the shapes of the distributions or the presence of outliers. 
Examples of Student Work at this Level The student does not make any reference to the shapes of the distributions or the presence of outliers in the selection of a measure of center. In addition, the student may:
 Choose measures of center to represent each distribution rather than one measure to compare.
 Suggest using the median because it will be the same for both classes.
 Compare the number of data points and notice the outlier but does not mention a measure of center.
 Suggest using the mean, â€śBecause it will show the most difference between the two.â€ť
 Not choose a measure of center but instead describes the shapes of the dot plots.
 Select one of the dot plots as the best measure of center.

Questions Eliciting Thinking Does it make sense to compare the mean of one distribution to the median of another?
What are measures of center? Do you know any examples of measures of center?
What did you mean by â€śit will show the most difference between the twoâ€ť?
Which class has a mean and a median that are different? Why do you think this happens?
How does the distribution of the data affect the mean? The median? 
Instructional Implications If needed, review terminology associated with the shapes of distributions such as symmetric, normal, skewed, and uniform. Show examples of each type and introduce the concept of an outlier.
Provide opportunities for the student to calculate both the mean and the median of a variety of distributions. Include symmetric, normal, skewed, and uniform data sets. For example, give the student five data points that are clustered close together in value and ask the student to find the median and the mean. Next, replace one of the data points with an extreme outlier. Again, ask the student to identify the median and compute the mean. Have the student compare the means and medians of the two related sets of data. Explain that the mean may not represent a typical score in the data set with an outlier, so the median may be a better choice of a measure of center. Make clear that the shape of a distribution and the presence of outliers should be taken into account when selecting an appropriate measure of center.
Discuss how the calculation of the mean and the median is related to the influence of outliers. Explain that since the calculation of the mean involves summing all of the values in the distribution, outliers contribute directly to its calculation. On the other hand, the median of a distribution such as {1, 2, 3, 4, 5} is unchanged if the final value, 5, is replaced by 100 since the median only takes into account the order of the data rather than the actual values. Have the student consider how outliers might affect the mode.
Provide additional opportunities to select measures of center to represent and compare distributions. Ask the student to justify all choices. 
Making Progress 
Misconception/Error The student selects a measure of center based on the shapes of the distributions but provides an incomplete justification. 
Examples of Student Work at this Level The student:
 Provides an adequate justification for using the median for Class A but says it should also be used for Class B because, â€śthe plots are closer together.â€ť
 Correctly suggests using the median but does not clearly explain that the median is more resistant to outliers such as the one in the Class A distribution.

Questions Eliciting Thinking What did you mean by â€śthe plots are closerâ€ť? How did this affect your choice of measure of center?
You said the distribution for Class A is skewed. Why is the median a better choice when the data is skewed?
You said the distribution for Class A contains an outlier. Why is the median a better choice when the data contains outliers? 
Instructional Implications Discuss how the calculation of the mean and the median is related to the influence of outliers. Explain that since the calculation of the mean involves summing all of the values in the distribution, outliers contribute directly to its calculation. On the other hand, the median of a distribution such as {1, 2, 3, 4, 5} is unchanged if the final value, 5, is replaced by 100 since the median only takes into account the order of the data rather than the actual values. Have the student consider how outliers might affect the mode.
Provide additional opportunities to select measures of center to represent and compare distributions. Ask the student to justify all choices. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student selects the median as a measure of center to compare the distributions and uses the shape of the distributions and the presence of the outliers in Class A to justify this choice. The student explains that, unlike the mean, the median is more resistant to outliers. The mean will be â€śpulledâ€ť toward the outliers.

Questions Eliciting Thinking Can you explain why the mean is more affected by outliers than the median? 
Instructional Implications Challenge the student to create three small sets of data: one in which the mean is less than the median, one in which the mean is greater than the median, and one in which the mean is equal to the median. Have the student relate the shapes of the distributions to each of these outcomes. 