Getting Started 
Misconception/Error The student is unable to explain how an outlier affects the mean. 
Examples of Student Work at this Level The student:
 Concludes that the mean is not affected by the outlier.
 Does not answer the question asked but attempts to determine the mean and median of the data set.

Questions Eliciting Thinking Did you answer the question asked? What is the question asking you to do? How would you describe the problem in your own words?
Do you know how to determine the mean of a set of data? How is the mean calculated?
Can you reason how this calculation might be affected by a value like 36 (without actually calculating the mean)? 
Instructional Implications Provide the student with direct instruction on the definitions for mean and outlier. For practice, ask the student to calculate the mean and median of three sets of data. Give the student one data set that does not contain an outlier, one set that contains an outlier smaller than the other elements in the set and one set that contains an outlier larger than the other elements in the set. Next, ask the student to determine and identify the outliers in the data sets. Finally, ask the student to compare the mean and the median for each data set and to analyze the relationship between the mean and the outlier. Ask the student to write a rule describing how an outlier affects the mean. Provide feedback as necessary. 
Making Progress 
Misconception/Error The student understands how an outlier affects the mean but makes a minor mistake or the explanation is unclear. 
Examples of Student Work at this Level The student:
 Writes a response that is vague or not specific.
 Writes a general response suggesting that the mean is always lower when an outlier is removed.
 Must calculate both means in order to write an answer.
 Quantifies the effect on the mean by suggesting the mean is greatly (or tremendously) affected by an outlier.

Questions Eliciting Thinking Your general response about how an outlier affects the mean is vague. Can you explain more clearly?
Your general response states that an outlier makes the mean higher â€śmost of the time.â€ť Is it possible for an outlier to make the mean lower? Can you give me a specific example?
I see that you calculated the mean of the data set both with and without the outlier. Could you have determined the effect the outlier would have on the mean without actually calculating it?
Your general response about how an outlier affects the mean is quantified as â€śtremendouslyâ€ť or â€śgreatly.â€ť Is there another way to describe how an outlier affects the mean? 
Instructional Implications Use a specific example to show the student how the calculation of the mean makes it vulnerable to the presence of outliers at either end of a distribution. Model explaining how, in general, the mean is affected by the presence of an outlier. For example, explain that the mean is â€śpulledâ€ť toward the outlier. Ask the student to attempt to explain why and provide feedback.
Address writing clear and concise responses to questions. Encourage the student to complete a careful review of responses, examining each sentence separately for accuracy and clarity. Ask the student to edit the response, so all pronouns are defined and details explained. Provide feedback as necessary. 
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 explains that the mean will be lower when the outlier, 36, is removed. The student is able to reason without actually calculating the mean. The student understands that, in general, the mean is increased or decreased by the presence of an outlier and that the mean is â€śpulled toward the outlier.â€ť 
Questions Eliciting Thinking Can you explain why the mean is pulled toward the outlier? What about the calculation of the mean makes it affected by outliers?
How is the median affected by outliers? 
Instructional Implications Challenge the student to make two dot plots for this data set, one with the outlier and one without the outlier. Ask the student to compare the mean, median, and mode for both data sets.
Challenge the student to determine when an element in a data set can be classified as an outlier. Ask the student to change the value of one element in a data set until the mean changes. Have the student increase the number of elements in the original set by replicating the median value. Ask the student to include the value that changed the mean in the first set to see if it also changes the mean in this larger data set. Tell the student to continue experimenting with data values and the number of elements in the data set to determine if there is a relationship between the number of elements in the set and the distance the outlier is from the majority of elements in the set. Ask the student to conjecture about the â€śstrengthâ€ť of an outlier based on the number of data points and the distance of the outlier from the majority of the other elements in the set. 