Data Displays     Conceptions of Statistics     Chance  

Unit 5

Investigating Chance



Unit 5, Investigating Chance, brings together all of the concepts from Units 1-4 to investigate chance. Students work with hand-held spinners and with TinkerPlots to explore the behavior of 2-color spinners. The purpose is to develop understanding of probability as a measure of uncertainty.The key idea is that the outcome of any single repetition cannot be known in advance,but with many repetitions, the uncertainty of particular outcomes can be measured.Students examine two complementary approaches to estimating probability, theoretical and empirical.They explore the probability of joint, independent outcomes, such as the sums of the outcomes of two spinners, from theseperspectives. The unit includes explorations of empirical approximations to the sampling distribution of one or more statistics, in light of changes in number of repetitions of a process (the sample size is the number of repetitions). The sampling distribution is the cornerstone of statistical inference. The Chance (Cha) and Conceptions of Statistics (CoS) constructs describe benchmarksof conceptual progress about probability and about the sampling distribution of a statistic.

Performances

COS4A: Predict that a statistic’s value will change from sample to sample.

COS4B: Predict that, while the value of a statistic varies from sample-to-sample, its behavior in repeated sampling will be regular and predictable.

COS4C: Predict and justify changes in a sampling distribution based on changes in properties of a sample (e.g., increase in the number of observations), or in the process generating the samples (e.g., some change that would influence the values of the sample statistic).

COS4D: Use statistics as measures of characteristics of sampling distribution. Anticipates effects of changes in generating process or sample size on these statistics.

CHA1B: View chance as describing particular outcomes, not a relative frequency of long-term occurrence.

CHA2B: View chance as related to repetition of trials.

CHA3B: Recognize the relation between relative proportions of possible outcomes and their likelihood.

CHA3C: Quantify probability as the ratio of the number of target outcomes to all possible outcomes (or as the ratio of areas representing these outcomes).

CHA4E: Use a statistic (e.g., mean or median) on sets of outcomes from repeated events to estimate the probability of a target outcome.

CHA5A: Construct a new variable by joining outcomes of events (i.e., create compound/ aggregate outcomes).

CHA5B: Describe a sample space by listing possible combinations of outcomes.

CHA5C: Describe a sample space by listing possible permutations of outcomes.

CHA6A: For compound (aggregate) events, relate sample space to probability.

MOV3A: Use chance devices to represent variability