Standard Essential Skills and Knowledge Clarification 8.SP.A.1: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Ability to integrate technology and relate the scenarios to authentic student-centered situations Ability to keep pairs of data organized in relation to one another within two sets of quantities bivariate data: When we conduct a study that examines the relationship between two variables, we are working with bivariate data. A study that examines a potential relationship between the height and weight of high school students is based on bivariate data, or two variables (height and weight). A study that looks at only one variable, for example a survey to estimate the average height of high school students is based on univariate data. scatter plot: Scatter are used to analyze patterns in . These patterns are described in terms of linearity, slope, and strength. Linearity refers to whether a data pattern is linear (straight) or nonlinear (curved). refers to the direction of change in variable y when the value of variable x increases. If the value of y also increases, the slope is positive; but if the value of y decreases, the slope is negative. If the data points are horizontal, the slope is 0. Strength refers to the degree of "scatter" in the plot. If the data points are widely spread, the relationship between variables is weak. If the points are concentrated around a line, clustered, the relationship is strong. Additionally, scatter can reveal unusual features in data sets, such as clusters, gaps, and . The scatter plots below illustrate some common patterns.
8.SP.A.2: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. See the skills and knowledge that are stated in the Standard. 8.SP.A.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Ability to integrate technology and to relate the scenarios to authentic student-centered situations bivariate measurement data: This refers to a relationship between two sets of data that can be evaluated by scales, as in a scatter plot. 8.SP.A.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on Ability to integrate technology and to relate the scenarios to authentic student-centered situations bivariate categorical data: This refers to a relationship between two sets of data that are descriptive. Analysis of categorical data generally involves the use of data tables. A two-way presents categorical data by counting the number of observations that fall into each group for two variables, one divided into rows and the other divided into columns. For example, a survey was conducted of a group of 20 individuals who were asked to identify their hair and eye color. A two-way table presenting the results might appear as follows: HAIR AND EYE COLOR