### DOE Archives

#### New Jersey Core Curriculum Content Standards

May 1996

Mathematics Standards And Progress Indicators
Standard 4.12:
All Students Will Develop An Understanding Of Statistics And Probability And Will Use Them To Describe Sets Of Data, Model Situations, And Support Appropriate Inferences And Arguments

Descriptive Statement: Probability and statistics are the mathematics used to understand chance and to collect, organize, describe, and analyze numerical data. From weather reports to sophisticated studies of genetics, from election results to product preference surveys, probability and statistical language and concepts are increasingly present in the media and in everyday conversations. Students need this mathematics to help them judge the correctness of an argument supported by seemingly persuasive data.

Cumulative Progress Indicators

By the end of Grade 4, students:

 1 Formulate and solve problems that involve collecting, organizing, and analyzing data. 2 Generate and analyze data obtained using chance devices such as spinners and dice. 3 Make inferences and formulate hypotheses based on data. 4 Understand and informally use the concepts of range, mean, mode, and median. 5 Construct, read, and interpret displays of data such as pictographs, bar graphs, circle graphs, tables, and lists. 6 Determine the probability of a simple event, assuming equally likely outcomes. 7 Make predictions that are based on intuitive, experimental, and theoretical probabilities. 8 Use concepts of certainty, fairness, and chance to discuss the probability of actual events.

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8, students:

 9 Generate, collect, organize, and analyze data and represent this data in tables, charts, and graphs. 10 Select and use appropriate graphical representations and measures of central tendency (mean, mode and median) for sets of data. 11 Make inferences and formulate and evaluate arguments based on data analysis and data displays. 12 Use lines of best fit to interpolate and predict from data. 13 Determine the probability of a compound event. 14 Model situations involving probability, such as genetics, using both simulations and theoretical models. 15 Use models of probability to predict events based on actual data. 16 Interpret probabilities as ratios and percents.

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 12, students:

 17 Estimate probabilities and predict outcomes from actual data. 18 Understand sampling and recognize its role in statistical claims. 19 Evaluate bias, accuracy, and reasonableness of data in real-world contexts. 20 Understand and apply measures of dispersion and correlation. 21 Design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes. 22 Make predictions using curve fitting and numerical procedures to interpolate and extrapolate from known data. 23 Use relative frequency and probability, as appropriate, to represent and solve problems involving uncertainty. 24 Use simulations to estimate probabilities. 25 Create and interpret discrete and continuous probability distributions, and understand their application to real-world situations. 26 Describe the normal curve in general terms, and use its properties to answer questions about sets of data that are assumed to be normally distributed. 27 Understand and use the law of large numbers (that experimental results tend to approach theoretical probabilities after a large number of trials).

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