Getting Started 
Misconception/Error The student does not address all of the key features of a distribution. 
Examples of Student Work at this Level The student organizes the data in a way that allows for the shape of the distribution to become evident but does not address all of the key features of the distribution: shape, center, and spread. For example, the student:
 Makes a dot plot and only describes where the data clusters.
 Makes a dot plot and only describes the center (incorrectly) and where the data clusters.
 Orders the data from least to greatest but gives no indication of the shape, center, or spread.

Questions Eliciting Thinking What are the key features of a distribution that should be included in its description?
How wouldÂ you describe the center of the data? Can you compute its median?
How would you describe the spread of the data?
Do you notice any outliers?
What is the overall shape of the data? Do you notice any clustering, peaks, or gaps? 
Instructional Implications Provide instruction on describing distributions. Explain that when describing a distribution, each of its key features (shape, center, and spread) should be addressed. If needed, review how to calculate measures of center (the mean, median, and mode) and spread (the range, interquartile range, and the mean absolute deviation) and guide the student to be specific about which measures have been reported when describing distributions. Review terminology used to describe the shape of a distribution (e.g., uniform, symmetric, bimodal, skewed left, and skewed right). Model describing each of the key features of the given distribution and then provide the student with additional opportunities to describe data distributions in context.
Consider using Illustrative Math http://www.illustrativemathematics.org/illustrations/1199 for further practice in describing data by center, spread, and shape within context. 
Moving Forward 
Misconception/Error The student describes the center, spread, and shape, but the descriptions contain some errors. 
Examples of Student Work at this Level The student organizes the data into a visual display and attempts to describe the shape, center, and spread but:
 Describes the center of the data as the value midway between 0 and 8.
 Confuses spread with the scale on the number line.

Questions Eliciting Thinking How did you calculate the center? Which measure did you use: the mean, median, or mode?
How can spread be described? What measure of spread could you use to describe this data?
What terms can be used to describe the shape of a distribution? 
Instructional Implications Review how to calculate measures of center (the mean, median, and mode) and spread (the range, interquartile range, and the mean absolute deviation) and guide the student to be specific about which measures have been reported when describing distributions. Review terminology used to describe the shape of a distribution (e.g., uniform, symmetric, bimodal, skewed left, and skewed right). Address specific errors in the studentâ€™s response. For example, explain that:
 The center of data refers to a typical value in the data set and not to the average of the extreme values.Â
 The â€śpeakâ€ť of the data refers to a value that occurs most often (e.g., has the greatest frequency) in the data set and is called the mode. The mode is not the greatest value in the data set. Clarify that there can be more than one mode, and distributions with two modes are often described as bimodal.
 The spread of data refers to the variability in the data set and not to the scale used in the dot plot.Â
Allow the student to revise his or her responses and provide additional opportunities to describe data distributions in context.
Consider using Illustrative Math http://www.illustrativemathematics.org/illustrations/1199 for further practice in describing data by center, spread, and shape within context. 
Almost There 
Misconception/Error The student does not use appropriate terminology to describe features of the distribution. 
Examples of Student Work at this Level The student:
 Uses the term â€śpeakâ€ť instead of mode.
 Is not specific about the measure of center or spread that he or she is reporting.
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 Does not use the term â€śskewâ€ť correctly to describe the shape.

Questions Eliciting Thinking What statistical term is the same as â€śpeak?â€ť
What measure of center did you calculate and describe?
What measure of spread did you calculate and describe?
Sometimes we say that a distribution is skewed right or skewed left? Which applies to this distribution? 
Instructional Implications Provide specific feedback to the student concerning ways in which his or her response could be improved and ask the student to revise his or her work. Model describing distributions using appropriate terminology. Provide the student additional opportunities to describe a variety of data distributions in context. 
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 organizes the data into a visual display (e.g., frequency table or dot plot) and describes the shape, center, and spread. For example, the student says:
 The distribution is skewed right which means that most of the data clusters around the values 0  2 but there are a few values from 3 â€“ 8.
 The median of the data is 1.
 The range of the data is 8 since values range from 0 to 8.Â

Questions Eliciting Thinking Do you see any evidence of an outlier?
Why did you choose to report the median instead of the mean?
What does this distribution indicate about the number of pets that Toryâ€™s classmates have? 
Instructional Implications Encourage the student to relate his or her description of the distribution to the context of the data to draw specific conclusions about the number of pets that Toryâ€™s classmates have. For example, model saying, â€śMost of the students in Toryâ€™s class have zero to two pets, a few have three or four pets, and one student has eight petsâ€ť or â€śthe median number of pets that Toryâ€™s classmates have is one pet while the mean is 1.6 pets.â€ť
Introduce the student to the concept of an outlier and explain that the student who has eight pets could be an outlier for this set of data. Have the student calculate both the median and the mean of the original set of data and, once more with the outlier removed. Encourage the student to observe the relative effect of the outlier on the mean and the median.
Consider implementing the MFAS tasks Math Test Center, Math Test Shape, and Math Test Spread (6.SP.1.2). 