Mathematics - Statistics

Index

Superintendent Letter
Mission Statement
Foreword
Introduction
Vocabulary

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Mathematics (Updated October 2003)

Mathematics - Statistics

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Goals and Descriptions

Data Analysis and Probability

PS1: DATA ORGANIZATION: FORMULATE
The learner will be able to formulate studies to answer question to real-world situations.

ллл	M.STAT.1.1 Sampling: Concepts The learner will be able to distinguish between sample and population, identify characteristics of representative samples to minimize bias and error, and recognize the variability among repeated samples taken from the same population.

ллл	M.STAT.1.2 Statistical Analysis: Estimate The learner will be able to develop the concept of estimating population parameters using confidence intervals produced from comparisons of box plots, and apply the capture-recapture model to generate a confidence interval for the populations.

ллл	M.STAT.1.3 Statistics: Models The learner will be able to develop estimates (both point and interval) for parameters (such as mean, standard deviation and proportion of successes) and test hypotheses concerning these parameters through the using appropriate statistical models.

лл	M.STAT.1.4 Sampling: \Construct The learner will be able to construct sampling distributions from binomial populations construct student experiments, random number tables and computer simulations.

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M.STAT.1.5 Mathematical Modeling: Simulation
The learner will be able to use the eight step process to build a model for simulating a given practical problem situation and use manipulatives, random number generators, calculators, and/or computers to perform the simulation to form an approximation to the problem solution.

л	M.STAT.1.6 Sampling: Concepts The learner will be able to understand the concept of randomness as applied to sample selection and identify other sampling methods suitable to given situations.

л	M.STAT.1.7 Data Collection: Methods The learner will be able to design a survey or an opinion poll or choose other methods of data to solve problems.

PS2: DATA ORGANIZATION: CONDUCT
The learner will be able to conduct investigations using statistical tools and display resulting data.

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M.STAT.2.1 Data: Organize/Summarize/Characterize
The learner will be able to organize, summarize, characterize, and interpret data from practical situations using relevant data sets by constructing of tables, graphs, and charts including frequency distributions, histograms, line plots, stem-and-leaf plots, box plots, and/or scatterplots for bivariate data.

лл	M.STAT.2.2 Sampling: Create The learner will be able to construct and interpret 90% and 95% box plots for various size samples, and use the box plots to summarize the sampling distribution.

лл	M.STAT.2.3 Central Limit Theorem: Use The learner will be able to apply the Central Limit Theorem and understand its impact on the distribution of the sample mean, including the effects of sample size.

лл	M.STAT.2.4 Data Collection: Experimental The learner will be able to collect and analyze data using experimental models and random number tables and generators.

лл	M.STAT.2.5 Simulations: Perform The learner will be able to perform simulations for problems where the probability of success is one-half and other then one-half and perform simulations for situations with an unknown number of key components.

PS3: DATA ANALYSIS: CENTRAL TENDENCY
The learner will be able to analyze real-world data collected using appropriate measures of central tendency and dispersion.

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M.STAT.3.1 Variation: Analyze Source
The learner will be able to analyze sources of variation and interpret and draw conclusions when solving applied problems. (Some may include the difference between samples and populations, sampling variability, the application of probability to make generalizations and predictions about populations based on the analysis of samples, the concept of random or chance variation, and analysis of variance).

лл	M.STAT.3.2 Data Analysis: Summarize The learner will be able to apply the measures of central tendency (mean, median, and mode), and measures of spread ( range, interquartile range, and standard deviation).

лл	M.STAT.3.3 Data Analysis: Recognize/Trends The learner will be able to identify trends in data represented graphically, including patterns, clusters, and outliers.

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M.STAT.3.4 Statistical Analysis: Alternative
The learner will be able to apply distribution-free or non-parametric methods as alternative to statistical analyses that make assumptions about populations sampled. (Applications from practical problems can be presented using such measures as the sign test, the Mann-Whitney U test and Sperman's rank correlation test).

PS4: DATA ANALYSIS: EVALUATE
The learner will be able to evaluate statistical studies and determine inferences that can be justified.

ллл	M.STAT.4.1 Data: Analyze Bivariate The learner will be able to analyze bivariate data represented graphically and predict results by fitting a line to the data, using methods such as mean fit and least squares and tools such as computers and calculators.

ллл	M.STAT.4.2 Correlation: Compute/Investigate The learner will be able to for a given bivariate scatter plot or data set, characterizes the correlation, calculates the correlation coefficient, and determine if a linear relationship exists.

ллл	M.STAT.4.3 Data: Linear Transformation The learner will be able to understand the effect of linear transformations have on the analysis and exploration of data.

ллл	M.STAT.4.4 Data Analysis: Interpret Out The learner will be able to interpret the outcome of data analysis and communicate these results.

л	M.STAT.4.5 Statistics: Proper/Improper The learner will be able to identify sound examples of statistics in decision making and correct the misuses of statistics.

л	M.STAT.4.6 Proof: Use/Mathematical Induction The learner will be able to use mathematical induction the derivation of certain formulas, the verification of appropriate properties, proofs of equivalence, and deductive reasoning.

PS5: PROBABILITY: COUNTING PRINCIPLES
The learner will be able to apply counting principles in real world contexts.

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M.STAT.5.1 Experiments: Apply Results
The learner will be able to use student-generate data sets, games of chance, manipulatives, and historic data to estimate probabilities with the empirical approach. Apply the results obtained from active experiments to illustrate the Law of Large Numbers and to develop the concept of theoretical probability.

л	M.STAT.5.2 Counting Methods: Apply The learner will be able to apply counting techniques and calculate the probability of the union and the intersection of two events, the probability of the complement, and conditional probability.

PS6: PROBABILITY
The learner will be able to apply the laws of probability in real world contexts.

ллл	M.STAT.6.1 Probability: Find/Odds/For/Associated The learner will be able to distinguish between odds for and probabilities and find the odds associated with given events.

ллл	M.STAT.6.2 Probability: Assign The learner will be able to assigns probabilities to the outcomes of a random variable and calculate expected value.

ллл	M.STAT.6.3 Probability Distributions: Distinguish The learner will be able to distinguishes between discrete and continuous distributions and solves problems using probability distributions, including binomial, normal, Poisson, and chi square.

лл	M.STAT.6.4 Probability: Geometric The learner will be able to use geometric probability to develop problem solving skills through experiments whose outcomes can be represented by points in a geometric region.

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