Getting Started 
Misconception/Error The student is unable to clearly describe the variable under investigation. 
Examples of Student Work at this Level The student is unable to discern the variable under investigation or to describe it completely. For example, the student describes the variable under investigation as:
 Feet.
 Depth.
 The number of lakes that are at a certain depth.
 The depth of the “lake” (singular) in feet.

Questions Eliciting Thinking What statistical question was asked that resulted in the data in the histogram?
What is meant by variable? What is meant by variable under investigation?
What exactly is being measured? How?
Can you describe the units of measure? How many lakes were measured? 
Instructional Implications Review the concept of a statistical question. Emphasize that in order to answer a statistical question, (1) data must be collected on more than one individual and (2) there must be an opportunity for the data to vary. Consider implementing MFAS tasks aligned to 6.SP.1.1 to assess the student’s understanding of statistical questions.
Next, focus instruction on how to determine and describe the variable under investigation from a graph. With reference to this task, explain that a scientist wanted to gain information about the depths of Florida lakes and measured the deepest point (in feet) of 50 randomly selected Florida lakes. The scientist then organized and displayed the data in the histogram. Explain that the range of depths (measured in feet), organized in equal groups or intervals, is displayed on the xaxis and the frequencies of each group or interval is displayed on the yaxis. Review that the histogram displays the shape of the frequency distribution, which can be used to answer statistical questions regarding the attribute under investigation.
Provide the student with a variety of graphs and ask the student to describe the variable under investigation including its unit of measurement. 
Making Progress 
Misconception/Error The student is unable to report the number of observations in a histogram. 
Examples of Student Work at this Level The student can describe the variable under investigation and how it is measured but does not understand how to interpret a histogram. The student:
 Thinks each bar (interval) represents a lake.
 Thinks the highest frequency, 16, represents the total number of lakes.

Questions Eliciting Thinking What do you think the heights of the bars represent?
What do the intervals on the horizontal axis of the histogram represent?
How many Florida lakes measure between 10 and 20 feet at their deepest point? How do you know? 
Instructional Implications Provide instruction on how to construct and read a histogram. Explain the distinction between categorical and quantitative data and be sure the student understands that histograms are used to display quantitative data while bar graphs are used to display categorical data. Emphasize that histograms are used to summarize the frequency of quantitative data that has been placed in intervals or classes of uniform width. Refer to the histogram in this task and explain the significance of each bar (e.g., the first bar on the left of the histogram indicates that the sample included three lakes with depths, d, at the deepest point in the interval 0 d < 10). Clarify for the student the actual widths of the intervals since the student may not understand the conventions for scaling the horizontal axis. Then ask the student how many lakes in the sample have depths between 10 feet and 20 feet (i.e., depths in the interval 10 d < 20). Guide the student to observe that the total number of lakes in the sample can be determined by summing the frequencies indicated by the heights of the bars. Explain that the histogram shows the deepest lake in the sample is between 70 and 80 feet deep (i.e., in the interval 70 d < 80) because the largest depth interval on the xaxis is 70 to 80 feet. Explain that most lakes in the sample are 20 to 30 feet deep (i.e., have depths in the interval 20 d < 30) because the bar representing that interval is the highest.
Provide the student with additional practice reading and interpreting histograms by posing questions that address interval widths, frequencies of data within intervals, the interval(s) of greatest or least frequency, the total number of observations, the overall shape of the histogram, and an interpretation of the distribution 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 clearly describes the variable under investigation as the depth, in feet, of the deepest point in Florida lakes and states that 50 lakes are represented in the histogram.

Questions Eliciting Thinking How would you describe the shape of this distribution?
Do you see any evidence of outliers? 
Instructional Implications Using the histogram in this task, have the student describe the symmetry and shape of the data distribution, and identify any possible outliers.
Provide opportunities for the student to construct histograms to display a set of given data. Ask the student to describe the distribution of the data by describing the shape, center, and spread as displayed in the histogram.
Consider using MFAS task Quiz Mean and Deviation (6.SP.2.5), Analyzing Physical Activity (6.SP.2.5), or Select the Better Measure (6.SP.2.5) to further assess the student. 