Getting Started 
Misconception/Error The student provides a vague or incomplete comparison of the distributions. 
Examples of Student Work at this Level The student compares the distributions without calculating both measures of center and spread. The student calculates and compares:
 Neither measure but draws an inference about the heights of the trees.
 Only the measures of center.
 Only the quartiles.

Questions Eliciting Thinking When comparing distributions, what are two features that can be addressed?
Which measure of center can you easily determine from a boxplot?
How does the spread of the two distributions compare? What does the spread of each distribution tell you about the heights of the trees?
You observed some differences in the box plots. Can you use those differences to compare the heights of the two types of trees? 
Instructional Implications Review the median as a measure of center and the interquartile range (IQR) as a measure of spread. If needed, provide instruction on how to calculate each value. Explain to the student that when comparing distributions, it is important to compare their centers, spread, and shape. Guide the student to draw comparative inferences about the two types of trees by comparing the centers and IQRs of the distributions of sample tree heights. Ask the student to revise his or her response to include addressing both features of a distribution.
Provide additional opportunities to draw informal comparative inferences about two populations using measures of center and spread of randomly selected samples. Consider implementing the MFAS task Word Length (7.SP.2.4). 
Making Progress 
Misconception/Error The student does not relate the comparison of the centers and spreads of the distributions to the context of the data. 
Examples of Student Work at this Level The student correctly calculates and compares the centers and spreads of the two distributions but does not relate this comparison to the context of the data (i.e., the heights of the trees). 
Questions Eliciting Thinking What is the context of this data? What statistical question did Jeremy pose that resulted in this data?
What does your comparison of the centers and spreads tell you about the two populations of trees? 
Instructional Implications Ask the student to explicitly describe the context of the data and the statistical question Jeremy posed that resulted in this data. Guide the student to use the comparisons of the centers and spreads to draw inferences about the heights of the trees. Ask the student to revise his or her response to include making inferences in context.
Provide additional opportunities to draw comparative inferences about two populations using measures of center and spread of randomly selected samples. Consider implementing the MFAS task Word Length (7.SP.2.4). 
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 better measure of center and variability for each distribution:
 For the first distribution, the student selects the median and the interquartile range because there are outliers and the median is not as affected by outliers as the mean. In addition, the median is used in the calculation of the interquartile range so it is a natural measure of variability to use when using the median. Also, since the calculation of the mean absolute deviation relies on the mean, then it is not the best choice of a measure of variability given that the mean is not the better choice of center.
 For the second distribution, the student selects the mean and mean absolute deviation because the distribution is symmetric and there are no outliers.

Questions Eliciting Thinking How do the outliers affect the mean?
How do the outliers affect the mean absolute deviation?
Why did you pick the interquartile range for Question 1?
You selected the mean and the mean absolute deviation for Question 2. Would you always select those two measures together? Why or why not? 
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. 