Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.
CT4ME has identified resources related to each benchmark of the Ohio Mathematics Academic Content Standards that students should have mastered by the end of the grades 8-10 program.
Identify the benchmark (A-K) for review in Data Analysis and Probability. Below each benchmark, you will find Web resources for reviewing the concept and practice problems.
Students should be able to review on their own using these resources. If you are not an Ohio educator, these resources can still benefit your test prep efforts, as benchmarks in other states are similarly stated.
Download the Test Prep Strand Booklet
Data Analysis and Probability (pdf) This test prep booklet (about 200 KB) is designed to help you monitor your progress toward mastery of each benchmark in this strand. You can print the entire booklet, or just those pages for benchmarks you need to work on. Write notes in the booklet next to each resource you use in your review.
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Other strand resources:
[ Number, Number Sense, and Operations ] [ Measurement ] [ Geometry and Spatial Sense ] [ Patterns, Functions, and Algebra ] [ Data Analysis and Probability ] [ Mathematical Processes ]
Benchmarks in this strand have been correlated to the Common Core State Standards (CCSS) for Mathematics for the Conceptual Category (CC), Domain (D), and Cluster (C).
NOTE: As a general resource for all Data Analysis and Probability benchmarks, students might consult the following resource:
Algebra from Oswego City School District (NY) Regents Exam Prep Center. Each sub-section includes lessons and interactive practice exercises. The probability and statistics strand has two sections: Working with Data and Probability.
A. Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.
CCSS: CC: Statistics and Probability, D: Interpreting Categorical and Quantitative Data, C: Summarize, represent, and interpret data on two categorical and quantitative variables.
CCSS: CC: grade 7, D: Statistics and Probability, C: Draw informal comparative inferences about two populations.
CCSS: CC: grade 8, D: Statistics and Probability, C: Investigate patterns of association in bivariate data.
NOTE: 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.
Bar graphs and circle graphs 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.
Scatter plots are used for experimental data to determine if there is a relationship between the variables studied.
When creating graphs, note the following 10 common errors, provided by CanTeach (CA):
Connexions: The basics about line graphs in representing data. Short module by David Lane of Rice University shows how line graphs compare to bar graphs and when to use line graphs. Two self-check questions included.
National Center for Education Statistics (for students): Create a Graph
Oswego City School District (NY), Intermediate Test Prep Center, Math 8:
Determine and justify the most appropriate graph to display a given set of data (pictograph, bar graph, line graph, histogram or circle graph)
Worsley School, Bill Willis: Box and Whisker Plots
Statistics Canada: Statistics, Power from Data: Graph Types and create your graph
Glencoe Online Study Tools, Mathematics, Algebra 2005, multiple choice practice:
NCTM E-examples: scroll down to 7.4: Line of Best Fit: Linear Regression and Least Squares
Prentice Hall: Using the TI-83 or TI-84 to perform a Linear Regression, Quadratic Regression, or Exponential Regression
Utah State University, National Library of Virtual Manipulatives:
Data Analysis and Probability Manipulatives--select by grade band
JAVA applet for Scatterplots from the Math Department at Hobart and William Smith Colleges: Launch the scatter plot, modify data and view the resulting line of best fit.
Play the video tutorials at the Ohio Resource Center for Mathematics, Science, and Reading:
Display Data for organizing information into tables and graphs with titles, legends, correct units, error bars, and fitting functions, video #18.
Lines of Fit for defining and finding lines of best fit using real data, video #26.
WASL 10-1-19: Box-and-Whisker Plots 2: Quick video on how to find the median from a box-and-whisker graph.
B. Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.
CCSS: CC: Statistics and Probability, D: Interpreting Categorical and Quantitative Data, C: Summarize, represent, and interpret data on a single count or measurement variable.
Statistical Graphs: Choosing an Appropriate Graph depends on the "type and breadth of the data, the audience it is directed to, and the questions being asked." Eleven graph types are discussed with advantages and disadvantages of each.
Oswego City School District (NY), Regents Prep, Algebra section: Displaying Data with lessons on histograms, quartiles and box and whisker plots, and practice with organizing and interpreting data.
Eduplace.com: Choosing an Appropriate Graph
Graphing Data for working with a spreadsheet to create different types of graphs with discussion of appropriateness, video #19.
C. Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.
CCSS: CC: grade 6, D: Statistics and Probability, C: Summarize and describe distributions.
CCSS: CC: grade 7, D: Statistics and Probability, C: Draw informal comparative inferences about two populations.
Statistics Canada: Statistics, Power from Data: Measures of Central Tendency
University of Illinois at Urbana-Champaign, Jay Hill: Introduction to Descriptive Statistics--mean, median, mode, range, and so on, simply explained.
BBC: Data Handling, the Mean, Median, and Mode
Mean, Median, and Mode: definitions and example of how to calculate each. This was posted from Nutshellmath.com
D. Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.
CCSS: CC: Statistics and Probability, D: Interpreting Categorical and Quantitative Data, C: Summarize, represent, and interpret data on a single count or measurement variable.
Shodor Interactive: Introduction to Statistics: Mean, Median, Mode
AlgebraLab.org: Mean, Median, Mode. Lesson, interactive online practice problems. Show the Related AlgebraLab documents for activities, additional practice problems and word problems.
Oswego City School District (NY), Regents Prep, Algebra section:
Glencoe Online Study Tools, Mathematics, Algebra 2005, multiple choice practice: Measures of Variation
Measures of Center and Dispersion for discussing the meaning of measures of center and using a calculator to explore measures of dispersion, video #25.
GCSE Maths Median and IQR: This short video shows how to find a median, lower quartile, upper quartile, then inter-quartile range.
E. Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.
CCSS: CC: Statistics and Probability, D: Making Inferences and Justifying Conclusions, C: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Glencoe Online Study Tools, IMPACT Mathematics, Course 1, multiple choice practice: Collecting and Analyzing Data
North Canton City Schools (OH): Misleading Graphs
F. Construct convincing arguments based on analysis of data and interpretation of graphs.
CCSS: CC: Statistics and Probability, D: Making Inferences and Justifying Conclusions, C: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
Interpret line graphs from the Earth Observatory at NASA. Analyze some temperature and precipitation graphs from different cities and match them up to the correct biome.
Glencoe Online Study Tools, Mathematics: Applications and Connections, Course 3, multiple choice practice: Misleading Graphs and Statistics
Glencoe Online Study Tools, IMPACT Mathematics, Course 3, multiple choice practice:
Edmonton Public Schools (CA), Jim Reed, Math 8: Problem Solving with Data, Reading and Interpreting Graphs
G. Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.
CCSS: CC: Statistics and Probability, D: Making Inferences and Justifying Conclusions, C: Understand and evaluate random processes underlying statistical experiments.
CCSS: CC: grade 7, D: Statistics and Probability, C: Use random sampling to draw inferences about a population.
Statistics Canada: Statistics, Power from Data: Sampling Methods
Edmonton Public Schools (CA), Jim Reed, Math 9: Interactive Sampling Terminology
Glencoe Online Study Tools, Mathematics, Algebra 2005, multiple choice practice: Sampling and Bias
H. Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.
CCSS: CC: Statistics and Probability, D: Conditional Probability and Rules of Probability, C: Use the rules of probability to compute probabilities of compound events in a uniform probability model.
Glencoe Online Study Tools, Mathematics: Applications and Connections, Course 3, multiple choice practice:
Glencoe Online Study Tools, Mathematics, Algebra 2005, multiple choice practice:
Oswego City School District (NY), Regents Prep, Algebra section:
Webmath.com: Permutations verify your list of permutations for up to 8 entries.
Probability Basics for exploring theoretical and experimental probability with tree diagrams and the fundamental counting principle, video #24.
Probability and Statistics: Review the counting principle and permutations. This was posted from Nutshellmath.com
I. Design an experiment to test a theoretical probability, and record and explain results.
CCSS: CC: Statistics and Probability, D: Use Probability to Make Decisions, C: Use probability to evaluate outcomes of decisions.
AlgebraLab.org: Law of Large Numbers and Simulations explains the process of experimental probability and suggests experiments to try. Be sure to show related AlgebraLab documents for additional lessons and practice problems in probability.
Glencoe Online Study Tools, Mathematics: Applications and Connections, Course 3, multiple choice practice: Using Sampling to Predict
J. Compute probabilities of compound events, independent events, and simple dependent events.
CCSS: CC: Statistics and Probability, D: Conditional Probability and Rules of Probability, C: Understand independence and conditional probability and use them to interpret data, and C: Use the rules of probability to compute probabilities of compound events in a uniform probability model.
CCSS: CC: grade 7, D: Statistics and Probability, C: Investigate chance processes and develop, use, and evaluate probability models.
What are the Odds? The Ins and Outs of Probability (by graduate students at University of Virginia): Take a nine-question interactive quiz assessing common probability misconceptions relating to compound and simple events, sample size, representativeness, and so on.
Glencoe Online Study Tools, Mathematics: Applications and Connections, multiple choice practice:
Course 2, Independent and Dependent Events
Course 3, Probability of Compound Events
Edmonton Public Schools (CA), Jim Reed, Math 8: Independent Events
Integrated Publishing: Dependent Events, explanation of probability and problems
GCSE Probability Part 1: This video is from a professor in Great Britain who nicely explains probability and shows examples: expected frequency, the typical problems involving picking balls from a bag, mutually exclusive events, independent events, and drawing diagrams to help identify possibilities.
Probability Part 2: tree diagrams. The same professor in Great Britain discusses the balls in a bag problems when making two picks, which leads to tree diagrams to help determine probability involving replacing after each pick, and then not replacing after a pick.
K. Make predictions based on theoretical probabilities and experimental results.
CCSS: CC: Statistics and Probability, D: Use Probability to Make Decisions, C: Calculate expected values and use them to solve problems.
Glencoe Online Study Tools, Mathematics: Applications and Connections, multiple choice practice:
Course 2, Theoretical and Experimental Probability
Course 3, Experimental Probability
Edmonton Public Schools (CA), Jim Reed, Math 9: Using Probability
Utah State University, National Library of Virtual Manipulatives: Box Model -- investigate theoretical and experimental probabilities.
Are you ready for the test?
Don't forget to review and complete the Six Steps for Success, including the full online practice tests.
Complete: Statistics, Data Analysis, and Probability Strand Questions using California's High School Exit Examination (CAHSEE) released questions.
Ohio Mathematics Academic Content Standards (2001). Retrieved from http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicID=1696&TopicRelationID=1704
Ohio Mathematics Academic Content Standards Crosswalk, K-8 and High School (2010). Retrieved from http://education.ohio.gov/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=1704&ContentID=83475
See
other strand resources:
[ Number, Number Sense, and Operations ] [ Measurement ] [ Geometry and Spatial Sense ] [ Patterns, Functions, and Algebra ] [ Data Analysis and Probability ] [ Mathematical Processes ]
See
related pages: [ Standardized Test
Preparation and Tips for Success (first page)] [ OGT Introduction ]
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Contact Dr. Patricia Deubel: deubelp@neo.rr.com
Last revised 03/13/12
CT4ME Author: Dr. Patricia Deubel
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