Getting Started 
Misconception/Error The student is unable to calculate and interpret the mean given data organized in a frequency table. 
Examples of Student Work at this Level The student:
 Does not know how to calculate or incorrectly calculates the mean.
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 Correctly calculates the mean but is unable to correctly interpret it.
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Questions Eliciting Thinking What do the numbers in the left column of the frequency table represent? What do the marks in the right column represent?
How many students scored 100? How do you know?
How is the mean calculated?
Is the mean a measure of center or a measure of spread?
What does the mean tell you about the set of scores? 
Instructional Implications If needed, provide instruction on how to construct and read a frequency table. Consider implementing the CPALMS Lesson Plan Calculating the Mean, Median, Mode, and Range from a Frequency Chart (ID 45979) to help the student read and use a frequency table.
Provide instruction on measures of center (mean and median) and what they indicate about a set of data. Explain that the mean is a measure of center and provides an indication of a typical, representative, or summary value from a set of data. Model interpreting the mean in context by saying, â€śThe scores of the 10 students tended to cluster around the mean of 80.â€ť Emphasize that the median, not the mean, is the value that separates scores into the upper and lower halves of the data. Using the quiz score data in the task, review how to calculate the mean and assist the student in showing appropriate work. When the student can demonstrate an understanding of the computational procedure, consider allowing the student to use a calculator to sum the scores and to divide by the number of scores.
Provide additional sets of data (both raw data and data given in frequency tables). Ask the student to calculate the mean and interpret its meaning in the context of the data. Provide feedback as needed. 
Moving Forward 
Misconception/Error The student is unable to calculate and interpret the mean absolute deviation. 
Examples of Student Work at this Level The student demonstrates an understanding of how to calculate and interpret the mean of the data but is unable to calculate the mean absolute deviation. The student:
 Does not know how to calculate or incorrectly calculates the mean absolute deviation.
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 Correctly calculates the mean absolute deviation but is unable to correctly interpret it.
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Questions Eliciting Thinking How do you find the absolute deviation of each number?
How do you calculate the mean absolute deviation?
Is the mean absolute deviation a measure of center or a measure of spread?
What does the mean absolute deviation tell you about the set of scores? 
Instructional Implications Provide instruction on measures of variability (mean absolute deviation and interquartile range) and what they indicate about a set of data. Explain that the mean absolute deviation represents the mean difference between individual data points and the mean and that a large mean absolute deviation indicates that there is a lot of spread or variability in the data. Model interpreting the mean absolute deviation in context by saying, â€śThe average deviation from the mean of 80 was 16 points.â€ť
Build on the studentâ€™s understanding of mean to explain how to calculate the mean absolute deviation. Assist the student in developing a system to organize data and calculations (e.g., a table with test scores on the left and absolute deviations from the mean on the right). Clarify that an absolute deviation is the absolute value of the difference between a data point and the mean, and the mean absolute deviation is the average of all absolute deviations.
Provide additional sets of data (both raw data and data given in frequency tables). Ask the student to calculate the mean absolute deviation and interpret its meaning in the context of the data. Provide feedback as needed. 
Almost There 
Misconception/Error The student is unable to identify an outlier and interpret its meaning in the context of the data. 
Examples of Student Work at this Level The student correctly calculates and interprets the mean and mean absolute deviation but is unable to identify an outlier or interpret its meaning in the context of the data. For example, the student:
 Identifies a value that is not an outlier (e.g., 50 because its frequency is zero or 100 because it has the greatest frequency).
 Identifies 40 as an outlier but does not explain its significance in context.
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Questions Eliciting Thinking What is an outlier?
Where will you find an outlier in a frequency table?
Why did you identify 40 is an outlier? What makes it an outlier? 
Instructional Implications Define outliers as extreme values or values that are much greater or much less than all the other values in a data set. Provide instruction on informally identifying outliers. Clarify that the largest and smallest value in a data set is not always an extreme value or outlier. Discuss how outliers and extreme values affect the mean. Identify 40 as a possible extreme value or outlier since it is so different from the next greatest score in the data set.
Provide additional sets of data (both raw data and given in frequency tables). Ask the student to identify any possible outliers and interpret their meaning in the context of the data. Provide feedback as needed. 
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 calculates the measures correctly and interprets their meaning in context:
 The mean score on the quiz is 80 which represents a typical score for the 10 students or is a value around which most of the scores cluster.
 Scores deviated from the mean of 80, on average, by 16 points.
 An extreme value is 40 since it is so different from the next greatest score in the data set.

Questions Eliciting Thinking What is the median and how does it compare to the mean?
What is the interquartile range and how does it compare to the mean absolute deviation?
If there were no outliers, do you think the median and interquartile range would represent the data better than the mean and mean absolute deviation? Why or why not? 
Instructional Implications Ask the student to remove 40 from the set of data and recalculate the mean and the mean absolute deviation of the scores. Ask the student to numerically describe the effect that the extreme value had on both the mean and the mean absolute deviation.
Consider administering other MFAS tasks. 