Iowa Core Curriculum - ..Data Analysis/Statistics And Probability

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Mathematics

Data Analysis/Statistics & Probability

Overall in the measurement strand, students should "understand measurable attributes of objects and the units, systems, and processes of measurement; and apply appropriate techniques, tools, and formulas to determine measurements." (NCTM, 2000, p. 44)

Statistics is the study of data; probability is the study of chance. These two topics are connected in the study of inferential statistics, in which one makes inferences that are based on data and qualified using probability. For example, suppose we want to compare the performance of two groups, each using a different mathematics program, on a standardized mathematics test. Data analysis methods are used to describe the test results for both groups, perhaps the mean is computed for each group. Then probability arguments are used to help us decide if the difference in means between the two groups is due to the intervention program or simply due to chance.

A key theme in the study of both statistics and probability is how to think about variability, in real data and in the outcomes of probabilistic situations, and how the notion of distribution helps organize thinking about variability. Statistical thinking should be emphasized when teaching, learning, and applying statistics and probability. Statistical thinking consists of formulating a good question, gathering data relevant to answering the question, analyzing the data, and drawing conclusions. The essential topics for statistics and probability are listed and discussed below.

Technology should be used appropriately to enhance and support the teaching and learning of statistics and probability. This may include judicious use of graphing calculators, interactive statistics software, and resources on the Internet. Such technology can be used, for example, to effectively apply simulation methods, analyze real-world data, and graphically represent concepts and methods of statistics and probability.

Essential Topics in Statistics and Probability

Descriptive statistics
Basic probability
Inferential statistics

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