Standardized Test Preparation and Tips for Success
Preparing Your Students for the Ohio Graduation Test
in Mathematics

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.

If needed, download Adobe Acrobat Reader, free software for viewing and printing PDF files.

You might need to download Java, a free plug-in from Sun Microsystems to interact with virtual manipulatives on this page.

Other strand resources:

[ Number, Number Sense, and Operations ] [ Measurement ] [ Geometry and Spatial Sense ] [ Patterns, Functions, and Algebra ] [ Data Analysis and Probability ]

What do we mean by Data and Probability?

Benchmarks in Data Analysis and Probability

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.

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.

Circle graphs and bar 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):

1. No title on graph
2. Source of data not given
3. Pictograph - no key
4. Scales are interrupted
5. Scales are not labelled
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

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: 

• Know how to create, read, and interpret graphs: circle, bar, histogram, line, pictograph, and stem and leaf

• 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:

• Box and Whisker Plots

• Histograms

• Statistics: Scatter Plots and Lines of Fit

NCTM E-examples: Line of Best Fit: Linear Regression and Least Squares

 

Utah State University, National Library of Virtual Manipulatives: 

• Data Analysis and Probability Manipulatives--select by grade band

• Box Plots and Histograms

• Scatterplots

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 video at YouTube.com:

• 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.

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: Collecting and Organizing Data

 

Eduplace.com: Choosing an Appropriate Graph

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.

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

 

Play video at YouTube.com:

• 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.

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, new Algebra section:

• Mean, Median, Mode 

• Quartiles and Percentiles

Glencoe Online Study Tools, Mathematics, Algebra 2005, multiple choice practice: Measures of Variation

 

Play video at YouTube.com:

• 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.

Glencoe Online Study Tools, IMPACT Mathematics, Course 1, multiple choice practice: Collecting and Analyzing Data

North Canton City Schools (OH):  Misleading Graphs

BBC: Data Handling, Interpreting Data

F.  Construct convincing arguments based on analysis of data and interpretation of graphs.

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.

 

South Dakota Department of Education: Graphs and Charts, Online Activities

 

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:

• Data Patterns in Tables and Graphs

• Models, Data, and Decisions

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.

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.

Glencoe Online Study Tools, Mathematics: Applications and Connections, Course 3, multiple choice practice:  

• Permutations 

• Combinations

Glencoe Online Study Tools, Mathematics, Algebra 2005, multiple choice practice:

• Counting Outcomes

• Permutations and Combinations

Oswego City School District (NY), Regents Prep:

• Counting Principle 

• Permutations 

• Combinations 

Webmath.com: Permutations  verify your list of permutations for up to 8 entries.

 

Play video at YouTube.com:

• 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.

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.

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

 

Play videos at YouTube.com:

• 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.

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.

Reference:

Ohio Mathematics Academic Content Standards. Available: http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEDetail.aspx?page=3&TopicRelationID=333&Content=13794 

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See other strand resources:

[ Number, Number Sense, and Operations ] [ Measurement ] [ Geometry and Spatial Sense ] [ Patterns, Functions, and Algebra ] [ Data Analysis and Probability ]