In this unit, students move from simply representing data into analysis of data. Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data. Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape. Throughout the module, students see and represent data distributions using dot plots and histograms. They study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution. As the unit ends, students synthesize what they have learned as they connect the graphical, verbal, and numerical summaries to each other within situational contexts.
6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.
6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.A.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:
Topic A: Understanding Distributions (6.SP.A.1, 6.SP.A.2, 6.SP.B.4, 6.SP.B.5b)
Lesson 1: Posing Statistical Questions
Lesson 2: Displaying a Data Distribution
Lesson 3: Creating a Dot Plot
Lesson 4: Creating a Histogram
Lesson 5: Describing a Distribution Displayed in a Histogram
Topic B: Summarizing a Distribution that is Approximately Symmetric Using the Mean and Mean Absolute
Deviation (6.SP.A.2, 6.SP.A.3, 6.SP.B.4, 6.SP.B.5)
Lesson 6: Describing the Center of a Distribution Using the Mean
Lesson 7: The Mean as a Balance Point
Lesson 8: Variability in a Data Distribution
Lesson 9: The Mean Absolute Deviation (MAD)
Lessons 10–11: Describing Distributions Using the Mean and MAD
Topic C: Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range
(6.SP.A.2, 6.SP.A.3, 6.SP.B.4, 6.SP.B.5)
Lesson 12: Describing the Center of a Distribution Using the Median
Lesson 13: Describing Variability Using the Interquartile Range (IQR)
Lesson 14: Summarizing a Distribution Using a Box Plot
Lesson 15: More Practice with Box Plots
Lesson 16: Understanding Box Plots
Topic D: Summarizing and Describing Distributions (6.SP.B.4, 6.SP.B.5)
Lesson 17: Developing a Statistical Project
Lesson 18: Connecting Graphical Representations and Numerical Summaries
Lesson 19: Comparing Data Distribution
Lesson 20: Describing Center, Variability, and Shape of a Data Distribution from a Graphical Representation
Lesson 21: Summarizing a Data Distribution by Describing Center, Variability, and Shape
Lesson 22: Presenting a Summary of a Statistical Project
Statistical Question (A question that anticipates variability in the data that would be collected in order to answer the question.)
Median (A measure of center appropriate for skewed data distributions. It is the middle value when the data are ordered from smallest to largest if there are an odd number of observations and half way between the middle two observations if the number of observations is even.)
Mean (A measure of center appropriate for data distributions that are approximately symmetric. It is the average of the values in the data set. Two common interpretations of the mean are as a “fair share” and as the balance point of the data distribution.
Dot Plot (A plot of numerical data along a number line.)
Histogram (A graphical representation of a numerical data set that has been grouped into intervals. Each interval is represented by a bar drawn above that interval that has a height corresponding to the number of observations in that interval.)
Box Plot (A graph of five numerical summary measures: the minimum, lower quartile, median, upper quartile, and the maximum. It conveys information about center and variability in a data set.
Variability (Variability in a data set occurs when the observations in the data set are not all the same.)
Deviations from the Mean (The differences calculated by subtracting the mean from the observations in a data set.)
Mean Absolute Deviation (MAD) (A measure of variability appropriate for data distributions that are approximately symmetric. It is the average of the absolute value of the deviations from the mean.
Interquartile Range (IQR) (A measure of variability appropriate for data distributions that are skewed. It is the difference between the upper quartile and the lower quartile of a data set and describes how spread out the middle 50% of the data are.