The following list provides outcomes that describe the knowledge and skills that students should understand and be able to do when the unit is completed. The outcomes are often components of more broadly-worded standards and sometimes address knowledge and skills necessarily related to the standards. The lists of outcomes are not exhaustive, and the outcomes should not supplant the standards themselves. Rather, they are designed to help teachers “drill down” from the standards and augment as necessary, providing added focus and clarity for lesson planning purposes. This list is not intended to imply any particular scope or sequence. S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). (additional) The student will: represent single count data using a plot appropriate to a given real-world scenario. S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. (additional) The student will: analyze the shape of a data distribution to determine if the mean or the median is the better statistic to use to represent the center. analyze the shapes of data distributions to compare the range, the interquartile range and standard deviation compare the center and spread of two or more data sets. S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (additional) The student will: compare two or more data sets using summary statistics appropriate to the shape of the data sets. explain the effects of extreme data points (outliers) on the summary statistics for a set of single count data. communicate what an analysis of the summary statistics of a set of single count data reveals. S.ID.5 Summarize for two categories in two-way frequency tables. Interpret relative frequencies in the context
S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. (major) Notes: Build on student experience with linear relationships in eighth grade and introduce the correlation coefficient. The focus here is on the computation and interpretation of the correlation coefficient as a measure of how well the data fit the relationship. The important distinction between a statistical relationship and a cause-and-effect relationship arises in S.ID.9. Knowledge of the range of the values ()and the interpretation of those values for correlation coefficients Ability to compute and analyze the correlation coefficient for the purpose of communicating the goodness of fit of a linear model for a given data set Use a scatter plot to check that the data appears to be linear. Only use “r” for linear relationships If all data points satisfy a linear equation (y=mx +b) then the value of r will be +1 (or -1)
given functions or choose a function suggested by the context. Emphasize linear and exponential models. marginal frequencies S.ID.5 Summarize for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data Marginal frequencies are frequencies that appear at the right and bottom margins of a two-way frequency table, representing the total row and total column entries. Student Activities
observational study See Clarifications/ Teacher Notes for S.ID.9 In an observational study a researcher observes subjects and measures variables of interest but does not attempt to influence the responses. Example: In an observational study a researcher is interested in finding a relationship between time spent memorizing a list of words and how many words the students can recall. Students are told to record the amount of time they spent memorizing the list and then the next day are asked to record as many words as they can recall. population See Clarifications/ Teacher Notes for S.ID.6 The entire set of items from which data can be selected is the population. For example, the population of all voters in a district, or a crop of apples that might be weighed or sorted in some manner. quantitative data See the third column of the “Unit 3 Snap Shot” Quantitative data consists of numbers representing counts or measurements. Mathematical operations can be performed on these in a meaningful way. Example: average height is quantitative relative frequency S.ID.5 Summarize for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data Relative frequency is the ratio of the actual number of favorable events to the total possible number of events; often taken as an estimate of probability Example: If a coin is tossed 50 times and the coin lands with Heads-up 30 times, the relative frequency with which a coin lands Heads-up in this experiment is .
In 7th grade students draw informal comparative inferences about two populations.(7.SP.3) In 8th grade students display frequencies and relative frequencies in two-way tables.(8.SP.4) Summarize for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. In Algebra II Unit 4 students make inferences and justify conclusions from sample surveys, experiments, and observational studies.(S.IC.1-6) In 6th grade students use variables to represent two-quantities that change in relationship to one another.(6.EE.9) In 8th grade students construct and interpret scatter plots and investigate patterns of association between the two quantities. (8.SP.1) Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. In Algebra II Unit 3 students will write functions that describe the relationship between two quantities. (F.BF.1)