In Thinking With Mathematical Models, students are introduced to a new idea related to judging what is typical of a distribution: a line of best fit. Use sentence stems and frames to support student discussion. The mean incorporates all values in a distribution and so is influenced by values at the extremes of a distribution. To ensure representative samples, we try to select random samples. The data collected, and the purpose for their use, influence subsequent phases of the statistical investigation. The sum of the probabilities of GGG, GGB, GBG, BGG is 4/8.) The … We can collect data about favorite types of books and report frequencies or relative frequencies in a bar graph of people liking mysteries, adventure stories, science fiction, and so on. Different questions elicit different types of data; we might ask questions that elicit numerical answers, or questions that elicit non numerical answers. Mathematics. Once a statistical question has been posed and relevant data types identified, the next step of an investigation is collecting data cases to study. A number of strategies for making random choices, such as drawing names from a hat, spinning spinners, tossing number cubes, and generating lists of values using a calculator or computer, are developed earlier in What Do You Expect? Questions may be classified as summary, comparison, or relationship questions. Raw data is data that has not been processed for use. Relationship questions are posed for looking at the interrelationship between two paired numerical attributes or between two categorical attributes. 11, 4, 27, 18, 18, 3, 24, 22, 11, 22, 18, 11, 18, 7, 29, 18, 11, 6, 29, 11. The MAD is the average distance between each data value and the mean, and is therefore only used in conjunction with the mean. Each individual family pattern is as likely as the others, so one can reason that each possibility has probability1/8. Raw Data. Raw data often is collected in a database where it can be analyzed and made useful. The graphs addressed in CMP3 serve three different purposes. In Thinking With Mathematical Models, students choose whether a line of best fit is an appropriate model. We can collect data about household size and organize them by frequencies in a line plot showing how many households have one person, two people, and so on. Modeling multiplicative situations with areas is used in several strands in CMP, from multiplication of fractions in Let’s Be Rational, to the Distributive Property in Prime Time or Frogs, Fleas and Painted Cubes, to computation of probabilities of compound events in What Do You Expect?, to illustrating completing the square in Function Junction. Understanding variability, the way data vary, is at the heart of statistical reasoning. You have a fixed and known numbered students in your class. The CCSSM content standards for grades 6–8 specify probability goals only in Grade 7. A simulation is an experiment that has the same mathematical structure as an activity or experiment of interest, but is easier to actually perform. Suppose we want number of students whose marks in 29. Consider these data: There are three interpretations of mean (or average) used in CMP. But the proportion of many such families that have no boys will be close to 1/8, the proportion that will have 1 boy will be close to 3/8, and so on. This generally means describing and/or comparing data distributions by referring to the following things: Each of these ideas is developed in a primary statistics Unit. In algebra, we solve equations to show things like, “If 7x + 5 = 47, then x = 6.” In geometry, we prove things like, “If the sides of a triangle are in the ratio 3:4:5, then it is a right triangle.” However, in many important quantitative reasoning tasks there is uncertainty in the If, then inferences that can be made. What are possible reasons why there is variation in these data? 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