Getting Started 
Misconception/Error The student is unable to calculate and interpret the median given data organized in a frequency table. 
Examples of Student Work at this Level The student:
 Visually inspects the frequency table and chooses a value near the middle.
 Calculates the median of the values in the table without regard to their frequency.
 Calculates the median or mean of the frequencies of the data.
 Attempts to calculate the mean.
 Counts the number of different values given in the table and determines this to be the median.
 Correctly calculates the median but is unable to correctly interpret it.

Questions Eliciting Thinking What do the numbers in the left column represent? What do the marks in the right column represent? How many students exercise 15 minutes per day? How do you know?
How is the median calculated?
Is the median a measure of center or a measure of spread?
What does the median tell you about this set of data? 
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 median is a measure of center and provides an indication of a typical, representative, or summary value from a set of data. Model interpreting the median in context by saying, “The median is the value in the middle of the data when it is organized from least to greatest. This means that half of the students exercise less than 25 minutes per day while the other half exercise more than 25 minutes per day.” If needed, review how to calculate the mean. Then using the data in the table, review how to calculate the median and assist the student in showing appropriate work.
Provide additional sets of data (both raw data and data given in frequency tables). Ask the student to calculate the median 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 interquartile range. 
Examples of Student Work at this Level The student demonstrates an understanding of how to calculate and interpret the median of the data but is unable to:
 Calculate the interquartile range.
 Interpret the interquartile range.

Questions Eliciting Thinking What are quartiles? How do you find them?
How do you find the interquartile range?
Is the interquartile range a measure of center or a measure of spread?
What does the interquartile range tell you about a set of data? 
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 interquartile range represents the range of the middle 50% of the values when the data is organized from least to greatest. Model interpreting the interquartile range by saying, “Fifty percent of the students exercise within a 42.5 minute range of each other (or 50% of the students exercise between 17.5 and 60 minutes per day).”
Build on the student’s understanding of median and the range to explain how to calculate the interquartile range. Ask the student to order the data from least to greatest and find the median. Then, show the student how to find the lower and upper quartiles. Define the lower quartile as the median of the lower half of the data, and the upper quartile as the median of the upper half. Explain that the quartiles separate the data into four groups each containing 25% of the data. Then define the interquartile range as the difference between the upper quartile and the lower quartile. Explain to the student that the interquartile range is a measure of the variability or range of the middle 50% of the data. It may be helpful to use a box and whisker plot to display the quartiles and the separation of the data.
Provide additional sets of data (both raw data and data given in frequency tables). Ask the student to calculate the interquartile range and interpret its meaning in the context of the data. Provide feedback as needed. 
Almost There 
Misconception/Error The student is unable to identify extreme values and interpret their meaning in the context of the data. 
Examples of Student Work at this Level The student correctly calculates and interprets the median and interquartile range but is unable to identify extreme values or interpret their meaning in the context of the data. For example, the student:
 Identifies zero and 180 as extreme values because they are the lowest and highest values.
 Identifies 20 as an extreme value because its frequency is the greatest.
 Identifies 120 and 180 as extreme values but is unable to explain why.

Questions Eliciting Thinking What is an extreme value or outlier?
Where will you find extreme values in a frequency table?
Why did you identify 120 and 180 as extreme values? What makes them extreme values? 
Instructional Implications Define extreme values and outliers as values that are much greater or much less than all the other values in a data set. Provide instruction on informally identifying extreme values and 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 120 and 180 as possible extreme values since they are at least twice as large as the next greatest value 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 median is 25. This means that half of the students exercise less than 25 minutes per day while the other half exercise more than 25 minutes per day.
 The interquartile range is 42.5. This means that 50% of the students exercise within a 42.5 minute range of each other (or 50% of the students exercise between 17.5 and 60 minutes per day).
 The outliers are 120 and 180. This means that two students exercise at least twice as long as any other student (or twice as long as the upper quartile).

Questions Eliciting Thinking What is the mean and how does it compare to the median?
What is the mean absolute deviation and how does it compare to the interquartile range?
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 Introduce the student to a test for outliers. For example, explain that any value that is greater than the or any value less than is often considered an outlier. Ask the student to use this test to determine if 120 and 180 are outliers.
Consider implementing the MFAS task Select the Better Measure (6.SP.2.5). 