Content Standard(s):
Mathematics 23. Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.
a. Determine which measure of center best represents a real-world data set.
b. Interpret the measures of center and variability in the context of a problem.
Unpacked Content
Evidence Of Student Attainment:
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. Teacher Vocabulary:
Data distribution
Measures of center
Measures of variability
Mean
Median
Mode
Interquartile range
Range Knowledge:
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. Skills:
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. Understanding:
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. Diverse Learning Needs:
Essential Skills:
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.
Prior Knowledge Skills:
Identify a numerical data set.
Calculate the range of data.
Organize numbers in a ordered list.
Calculate the mean, median, and mean of a data set.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 24. Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.
a. Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).
b. Use graphical representations of real-world data to describe the context from which they were collected.
Unpacked Content
Evidence Of Student Attainment:
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. Teacher Vocabulary:
Dot plots
Histograms
Box plots
Stem and leaf plots
Line plots
Extreme values
Outliers
Gaps
Clusters
Symmetric
Skewed
Center
Spread
peaks
5 number summary
Minimum
Maximum
Median
lower quartile
Upper quartile Knowledge:
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. Skills:
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. Understanding:
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. Diverse Learning Needs:
Essential Skills:
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.
Prior Knowledge Skills:
Identify different types of graphs.
Create a bar graph and box plot.
Organize data in an ordered list.
Alabama Alternate Achievement Standards
AAS Standard:
