ALEX Classroom Resource

Students:
Given a set of numerical data, summarize the data by,

• Reporting the number of observations (n).
• Describing the nature of the attribute under investigation.
• Calculating, interpreting, and comparing the measures of center (median/mean/mode) in a real-world data set,
• Calculating, interpreting and comparing the measures of variability (interquartile range and range) in a real-world data set.
• Given a set of numerical data interpret the measures of center and variability in the context of a problem.
• Justify their choice of measures of center and variability to describe the data based on the data distribution and the context in which the data were gathered.

Students know:

• Measures of center and how they are affected by the data distribution and context.
• Measures of variability and how they are affected by the data distribution and context.
• Methods of determining mean, median, mode, interquartile range, and range.

Students are able to:

• Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
• Determine measures of center and variability for a set of numerical data.
• Use characteristics of measures of center and variability to justify choices for summarizing and describing data.

Students understand that:

• Measures of center for a set of data summarize the values in the set in a single number and are affected by the distribution of the data.
• Measures of variability for a set of data describe how the values vary in a single number and are affected by the distribution of the data.

Learning Objectives:
M.6.23.1: Define numerical data set, measure of variation, and measure of center.
M.6.23.2: Relate the measure of variation, of a data set, with the concept of range.
M.6.23.3: Relate the measure of the center for a numerical data set with the concept of measure of center.
M.6.23.4: Define numerical data set, quantitative, measure of center, median, frequency distribution, and attribute.
M.6.23.5: Compare and contrast the center and variation.
M.6.23.6: Collect the data.
M.6.23.7: Organize the data.
M.6.23.8: Describe how attribute was measured including units of measurement.
M.6.23.9: Identify the attribute used to create the numerical set.

Students:
Given a set of numerical data,

• Analyze graphical representation of data by describing the center, spread, and shape including approx. symmetric or skewed.
• Reporting significant features in the shape of data including striking deviations, (e.g., extreme values, outliers, gaps, and clusters).
• Organize and display the data using plots on line plots, dot plots, stem and leaf plots, histograms, and box plots.

Students know:

• How to use graphical representations of real-world data to describe context, center, spread and shape from which they were collected.
• Techniques for constructing line plots, stem and leaf plots, dot plots, histograms, and box plots.

Students are able to:

• Organize and display data using dot plots, line plots, stem and leaf plots, histograms, and box plots.
• Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
• Describe the shape of numerical data distribution including patterns and extreme values.
• Use graphical representations of real-world data to describe and summarize the context from which they were collected.

Students understand that:

• Sets of data can be organized and displayed in a variety of ways, each of which provides unique perspectives of the data set.
• Data displays help in conceptualizing ideas and in solving problems.
• The overall shape and other significant features of a set of data, (e.g., gaps, peaks, clusters and extreme values) are important in summarizing numerical data sets.

Learning Objectives:
M.6.24.1: Define dot plots, line plot, stem and leaf plots, upper quartile, lower quartile, median, histograms, and box plots.
M.6.24.2: Recall how to read a graph or table.
M.6.24.3: Calculate upper quartile median, lower quartile median, overall median, greatest value, and lowest value.
M.6.24.4: Create box plot using calculations.
M.6.24.5: Plot data on dot plots and histograms.
M.6.24.6: Construct and label the display.
M.6.24.7: Recognize the different types of displays.
M.6.24.8: Define distribution and skew.
M.6.24.9: Describe the shape of a set of data in a given distribution.
M.6.24.10: Describe the spread of a set of data in a given distribution.
M.6.24.11: Describe the center of a set of data in a given distribution.