Getting Started 
Misconception/Error The student cannot correctly identify the median and the interquartile range. 
Examples of Student Work at this Level The student:
 Identifies incorrect values of the median and IQR for one or both distributions.
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 Indicates that he or she does not know how to identify the median and IQR from a box plot.

Questions Eliciting Thinking If you had the data in front of you, would you be able to find the median and IQR? How is a box plot created? What do you need to know about a distribution to make a box plot? 
Instructional Implications If needed, review how to find the median and the quartiles of a set of data. Be sure the student understands that the median is the same as the second quartile and should be found first; the other quartiles can be found by finding the median of the lower half of the data and the median of the upper half of the data. Explain that the quartiles divide the data into four groups each containing 25% of the data. Then show the student how to calculate the IQR. Emphasize that the IQR describes the range of the middle 50% of the data. Explain that a small IQR indicates that there is very little spread in the middle portion of the data and a large IQR indicates that there is a lot of spread in the middle portion of the data. Remind the student that the IQR is a good measure of spread when the median is used as a measure of center and when there are outliers in the data.
Review the fivenumber summary (which includes the lowest value, the three quartiles, and the highest value in a set of data) and how the summary is used to construct a box plot. Indicate that box plots always contain an axis with a scale so that the values can be interpreted. Ask the student to find the median of the two given data sets along with the other quartiles and to calculate the interquartile ranges of each distribution. Provide additional data sets and ask the student to calculate the fivenumber summary and construct box plots. 
Moving Forward 
Misconception/Error The student is unable toÂ describe the difference between the medians as a multiple of the interquartile range. 
Examples of Student Work at this Level The student correctly identifies the medians and the interquartile ranges (IQR) of each distribution, but is unable to describe the difference in the medians as a multiple of the IQR. The student:
 Only observes that the IQRs are the same while the medians are different.
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 Calculates the difference in the medians but can go no further.
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 States that neither median is a multiple of the IQR.
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Questions Eliciting Thinking What is the difference between the medians of the two box plots?
What does the term multiple mean?
How is this difference related to the IQR? 
Instructional Implications Explain that the purpose of the third question is to assess the degree of overlap between the two distributions. Review the meaning of the term multiple and pose problems in which the student must write one number as a multiple or product of another. For example, ask the student to write 30 as a multiple of five by writing 30 = 6 x 5 or as a product ofÂ 120 and another number by writing 30 = x 120. Then guide the student through the process of writing the difference between the medians, four, as a multiple of the IQR, 16. Assist the student in understanding that since four is smaller than 16, four is a fraction of 16.
Provide additional sidebyside box plots (with similar spread and different medians) and ask the student to describe the difference between the medians as a multiple of the IQR.
Consider implementing MFAS tasks TV Ages  2 and/or Comparing Test Scores (7.SP.2.3). 
Almost There 
Misconception/Error The student makes an error when describing the difference between the medians as a multiple of the interquartile range. 
Examples of Student Work at this Level The student correctly identifies the medians and IQRs of each distribution, but:
 Writes the IQR as a multiple of the median.
 Does not explicitly describe the difference between the medians as a multiple of the IQR (e.g., the student only writes â€ś16 = 4 x 4â€ť).
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Questions Eliciting Thinking It looks like you wrote the IQR as a multiple of the difference between the medians. Can you write the difference between the medians as a multiple of the IQR?
How many IQRs apart are the two medians?
What part of your work represents the multiple? Can you write out your final answer in a summary statement? 
Instructional Implications Provide feedback to the student concerning any error made and ask the student to revise his or her work. Ask the student to summarize the final answer in a sentence in order to make clear what value represents the multiple the student was asked to find. If needed, explain to the student that the objective was to assess the degree of overlap between the two distributions. Assist the student in interpreting the multiple as a measure of the degree of overlap (e.g., explain that a small multiple indicates that there is more overlap between the two distributions so that differences between their centers are likely to be small and insignificant).
Consider implementing MFAS tasks TV Ages  2 and/or Comparing Test ScoresÂ (7.SP.2.3). 
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 indicates the following:
 The median of the 1217 age group is 18 and the median of the 1824 age group is 22.
 The IQR of each age group is 16.
 The difference between the medians is four, which is of the IQR, 16.
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Questions Eliciting Thinking What do you think this indicates about the differences between the two distributions?
What does the multiple you found indicate about the degree of overlap of the two distributions?
Are there any other differences evident between the two distributions? 
Instructional Implications Challenge the student to find a way to describe the difference between the medians of two distributions in terms of a measure of spread when the distributions do not have the same IQR (e.g., ask the student to suppose that the IQRs of the two given distributions were 8 and 20, respectively, and to determine a suitable value to represent the spread of the two distributions).
Have the student compare the two distributions in terms of their centers, spread, and shape. Ask the student to reference the context of the data in the comparison.
Consider implementing MFAS task Comparing Test Scores (7.SP.2.3). 