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Common Core High School Statistics & Probability Teaching and Learning Resources

Domain: ID: Interpreting Categorical and Quantitative Data

Common Core Math

Select the cluster for resources on this page:

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ID-A: Summarize, represent, and interpret data on a single count or measurement variable

Standards:

 

Technology-enhanced investigations:

Mathwords.com: Math Dictionary.  Note: Terms followed by * are defined at MathsIsFun.com.  Also see the Stattrek.com Statistics Dictionary for terms followed by **.  Key vocabulary for this domain.  Use with ID-A, ID-B, ID-C:

bivariate and univariate data* histogram* linear fit regression equation
box plot mean normal distribution* scatterplot
box-and-whisker plot median outlier standard deviation*
correlation coefficient mode quartiles slope
dot plot* interquartile range first quartile stemplot
frequency table** 2-way table** third quartile joint
frequency**
marginal
frequency**
conditional
frequency**
relative
frequency**
 

 

Academo.org: Standard Deviation Calculator.  After entering the numbers, this tool shows the number of numbers, the mean, variance, and standard deviation.  A brief explanation of the standard deviation formula is included.  Aligns with ID-A.2 and ID-A.4.

Alcula.com:

BBC GCSE Bitesize Maths, Statistics and Probability: Averages: Mean, Mode, and Median --There is an explanation (called Revise), activity, and test.

Calculator.net: The following also includes explanations of theory for each calculator

CalculatorSoup: Descriptive Statistics Calculator.  A complete calculator showing min, max, range, mean, median, mode, standard deviation, variance, quartiles, interquartiles, outliers, and more.  A frequency table is also shown.  Aligns with ID-A.2.

College Preparatory Math: Student Tutorials: TI-84 Graphing Calculator: Univariate Data: Videos and screen shots illustrating use of the calculator to set up histograms, box plots, comparing two box plots, and summarizing data numerically.  Use with ID-A.1.

LearnZillion:

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary.  Flaws of Averages: "This learning video presents an introduction to the Flaws of Averages using three exciting examples: the “crossing of the river” example, the “cookie” example, and the “dance class” example. Averages are often worthwhile representations of a set of data by a single descriptive number. The objective of this module, however, is to simply point out a few pitfalls that could arise if one is not attentive to details when calculating and interpreting averages."  Aligns with ID-A.2.

National Library of Virtual Manipulatives: Box Plots and Histograms (Java required). Use with ID-A.1.

National Center for Education Statistics: Create a graph

Ohio Resource Center on YouTube: Tutorials for High School Mathematics.  Select the following:

OnlineStatBook: Graphing Distributions is a chapter that addresses stem and leaf displays, histograms, frequency polygons, box plots, dot plots, bar charts, line graphs, and more.  Exercises are included.  The project to develop the book was led by David Lane at Rice University.

PhET Interactive Simulations: Plinko Probability. Per its description: "Drop balls through a triangular grid of pegs and see them accumulate in containers. Switch to a histogram view and compare the distribution of balls to an ideal binomial distribution. Adjust the binary probability and develop your knowledge of statistics!"  Aligns with ID-A.1, ID-A.2, and IC-A.2.

Purple Math:

Shodor Interactivate: Statistics and Probability: Interpreting Categorical and Quantitative Data: Summarize, represent, and interpret data on a single count or measurement variable.  A series of nine lessons and 14 activities with virtual manipulatives to investigate concepts such as box plots, histograms, stem-and-leaf plots, measures of center and spread, the Bell curve, univariate and bivariate data, normal distributions, skewed distributions.  Aligns with ID-A. 

Stat Trek: Tutorials:

Statistics Canada: Statistics, Power from Data:

Thinking Mathematics: Standard Deviation Formula Explained: A YouTube video.  Aligns with ID-A.2 and ID-A.4.

University of Illinois at Urbana-Champaign, Jay Hill: Introduction to Descriptive Statistics--mean, median, mode, central tendency, variation, range, variance, and standard deviation, simply explained.

Teaching Channel Video: Statistical Analysis to Rank Baseball Players:  This video's lesson objective: Rank the greatest NY Yankee homerun hitters using statistical analysis.  Questions for learners to consider are included.  Use to address ID-A.1, ID-A.2, and ID-A.3.

Online Statistics Calculators:  There are five calculators available for measures of central tendency and dispersion, box and whisker plots, linear regression, correlation coefficients, and scatter-plots.  Aligns with ID-A.1 and ID-A.2.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 14 manipulatives addressing ID-A.1, 5 manipulatives for ID-A.2, 9 manipulatives for ID-A.3, 12 manipulatives for ID-A.4.  Among those:

YouTube video: GCSE Maths Median and IQR: This short video shows how to find a median, lower quartile, upper quartile, then inter-quartile range.

Multiple Choice:

MathBitsNotebook: Algebra 1: Statistics: Data Distributions includes lessons, then practice problems on categorizing data, box plots, outliers, measures of center and shapes of distributions, standard deviation, and interpreting graphs.  Use with ID-A.1, ID-A.2, and ID-A.3.

MathsIsFun.com:

Constructed-response:

AlgebraLab.org: Mean, Median, Mode.  Lesson, interactive online practice problems.  Show the Related AlgebraLab documents for activities, additional practice problems and word problems.  Aligns with ID-A.2.

Khan Academy: Analyzing Categorical Data unit. Practice questions with videos.

Statistics: Power from Data:

Zweigmedia.com:  Tutorials and examples using fill-in or multiple choice to test understanding.  Learners can also choose to do game versions of some topics.  Use with ID-A:

Performance tasks:

Illustrative Mathematics: Statistics and Probability:

Mathematics Assessment Project: Standards: High School: Statistics & Probability:

Mathematics Vision Project, Secondary 1 Student Edition:

Mathematics Vision Project, Secondary 3 Student Edition:

NCTM's Reasoning and Sense Making Task Library: Eruptions: Old Faithful includes the task overview, teacher notes for its use in the classroom, and student activity sheet.  Aligns with IC-A.1, ID-A.1, and mathematical practice standards 1, 3, and 5.

Statistics in Schools from the U.S. Census Bureau: Activities: Math: 9-12:

 

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ID-B: Summarize, represent, and interpret data on two categorical and quantitative variables

Standards:

Notes:

Each type of graph has its advantages and disadvantages.

Line graphs and histograms are only used with continuous data, which means that theoretically all values are possible (no gaps) in an interval (between any two it is possible to get another).  Examples include height, weight, time to complete your homework, and time to complete a trip.  Line graphs are good to demonstrate trends, such as sales in a company over time or changes in temperature over time.

Line graph example showing temperatures on December 1

Histogram example for heights of students

Bar graphs and circle graphs (often called pie charts) are only used with discrete data, which means that only certain values (gaps) are possible. Examples typically include counting, as in the number of students in a class, the number of crimes reported to the police, or the number of tickets sold to a game.  Note that pie charts are good for presenting percentages.  Bar graphs can be presented vertically or horizontally.  For example, a horizontal bar graph could be used to compare expenses among four departments of a company.

Bar graph example with basketball ticket prices for six schools

Circle graph example with 24 hour time budget for an average school day

Scatter plots are used for experimental data to determine if there is a relationship between the variables studied.

Three Scatter Plot Examples with Correlation

When creating graphs, note the following 10 common errors, provided by CanTeach (CA):

  1. No title on graph
  2. Source of data not given
  3. Pictograph - no key
  4. Scales are interrupted
  5. Scales are not labeled
  6. Symbols in pictographs not same size or equally spaced on graph
  7. Use of 2 or 3 dimensional objects to compare data (area/volume)
  8. Scales do not start at zero
  9. Numbers on axis (vertical or horizontal) not equally spaced
  10. Scale is selected to produce desired result

 

Technology-enhanced investigations:

Alcula.com:

CK-12: Algebra: Concepts, video, and practice problems for learners.

College Preparatory Math: Student Tutorials: TI-84 Graphing Calculator: Bivariate Data: Videos and screen shots illustrating use of the calculator for setting up a scatter plot, non-linear regressions, least squares regression line, the correlation coefficient, residuals & residual plots.

LearnZillion:

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary.  Flu Math Games: "This video lesson shows students that math can play a role in understanding how an infectious disease spreads and how it can be controlled."  Additional simulations are included.  Aligns with Algebra standards SSE-B.3.c and REI-A.1; Function standards IF-C.8.b, BF-B.4.a, and LE-A-1.(a, c); and Statistics and Probability standards ID-B.6.a, IC-A.1, IC-B.4, CP-A.2, and MD-A.1.

National Library of Virtual Manipulatives: Scatterplots (Java required).

NCTM Illuminations:

Ohio Resource Center on YouTube: Tutorials for High School Mathematics: Lines of Fit: Defining and finding lines of fit using real data.

PhET Interactive Simulations:

Saltire Software: Common Core Nuggets: There are five applets addressing residual plots and least squares, which align with ID-B.6.

Shodor Interactivate:

Stat-Trek: Tutorials:

Thinking Mathematics: Line of Best Fit: Least Squares Method: Video with explanations on why we calculate the line of best fit the way we do, and the mathematics behind the formula for the best line fitting data on a scatter plot.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 1 manipulative addressing ID-B.5, 20 manipulatives for ID-B.6.  Among those:

Multiple Choice:

MathsIsFun.com: Scatter Plots: Contains a concise explanation of the scatter plot and its relation to line of fit and correlation.  Following the explanation are nine multiple choice exercises.  Use with ID-B.6.

Khan Academy: Exploring Bivariate Numerical Data unit. Practice questions with videos.

MathBitsNotebook: Algebra 1: Statistics: Bivariate Data includes lessons, then practice problems on two-way frequency tables, fitting functions to data, residuals, linear regression, correlation and correlation coefficients, slopes and intercepts of linear models.  Use with ID-B.5, ID-B.6, ID-C.7, ID-C.8, and ID-C.9.

Constructed-response:

Khan Academy:  Summarizing quantitative data unit.  Practice questions with videos.

The Math You Need, When You Need It: Constructing a line of best fit includes tutorials followed by practice problems focusing on real-life scenarios on this topic that geoscientists would encounter.  The site is by SERC, the Science Education Resource Center at Carleton College.

Zweigmedia.com: Tutorials and examples using fill-in to test understanding.  Learners can also choose to do game versions of some topics.  Use with ID-B.6: Linear regression

Performance tasks:

Illustrative Mathematics: Statistics and Probability:

Inside Mathematics: MARS Tasks: The following align with ID-B.6:

Mathematics Assessment Project: Standards: High School: Statistics & Probability:

Mathematics Vision Project, Secondary 1 Student Edition: Module 8: Modeling Data: This module contains eight classroom tasks.  Module 8 addresses standards ID-A.1, ID-A.2, ID-A.3 and ID-B.5, ID-B.6 and ID-C.7, ID-C.8.  Task 3: After School Activity; and Task 4: Relative Frequency align to standard ID-B.5.  Task 7: Getting Schooled; and Task 8: Rocking the Residuals align to standard ID-B.6.

Statistics in Schools from the U.S. Census Bureau: Activities: Math: 9-12:

 

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ID-C: Interpret linear models

Standards:

 

Technology-enhanced investigations:

Khan Academy:

LearnZillion:

PhET Interactive Simulations: Least-Squares Regression.  Aligns with ID-B.6, ID-B.6.a, ID-B.6.b, ID-B.6.c, and ID-C.8.

Stat Trek: Tutorial: Linear Correlation Coefficient: The tutorial includes a video, and explanation on how to interpret and calculate the correlation coefficient.   Use with ID-C.8.

Social Science Statistics: Pearson Correlation Coefficient Calculator.  Free online calculator.  Use with ID-C.8.

College Preparatory Math: Student Tutorials: TI-84 Graphing Calculator: Bivariate Data: Videos and screen shots illustrating use of the calculator for setting up a scatter plot, non-linear regressions, least squares regression line, the correlation coefficient, residuals & residual plots.

Wolfram Alpha: Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 3 manipulatives for ID-C.8.  Among those:

Multiple Choice:

Khan Academy: Exploring Bivariate Numerical Data unit.  Practice questions with videos.

MathBitsNotebook: Algebra 1: Statistics: Bivariate Data includes lessons, then practice problems on two-way frequency tables, fitting functions to data, residuals, linear regression, correlation and correlation coefficients, slopes and intercepts of linear models.  Use with ID-B.5, ID-B.6, ID-C.7, ID-C.8, and ID-C.9.

MathsIsFun.com: Correlation: Contains a concise explanation of the meaning of correlation, correlation does not mean causation, and how to calculate the correlation coefficient.  Worked examples are provided.  Following the explanation are four multiple choice exercises.  Use with ID-C.8 and ID-C.9.

Constructed-response:

 

Performance tasks:

Illustrative Mathematics: Statistics and Probability:

Mathematics Assessment Project: Standards: High School: Statistics & Probability: Task 217: Interpreting Statistics: A Case of Muddying the Waters

Mathematics Vision Project, Secondary 1 Student Edition: Module 8: Modeling Data: This module contains eight classroom tasks.  Module 8 addresses standards ID-A.1, ID-A.2, ID-A.3 and ID-B.5, ID-B.6 and ID-C.7, ID-C.8.  Task 5: Connect the Dots aligns to standard ID-C.8. Task 6: Making More $; and Task 7: Getting Schooled align to both standards ID-C.7, ID-C.8.

Statistics in Schools from the U.S. Census Bureau: Activities: Math: 9-12:

 

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Common Core Math: Intro | HS Statistics & Probability Domain: ID  |  IC  |  CP  |  MD  |