Statistics (Inferences from Data)

8 Components
Initial Task
Animals
Big Ideas
Big Idea 1 Big Idea 2 Big idea 3
Formative Assessment Lesson
A Case of Muddying the Waters
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources ALG II Unit 6 Find aligned Regents questions with Quiz Banker
A2 U6: Statistics (Inferences from Data)
Browse Components
Initial Task
Animals
Big Ideas
Big Idea 1 Big Idea 2 Big idea 3
Formative Assessment Lesson
A Case of Muddying the Waters
Re-engagement
End of Unit Assessments
End of Unit Assessment for Unit 6 End of Unit Assessment Teacher Resources ALG II Unit 6 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 2

Visual models illustrate the correlation of bivariate data.

1 week
See Standards
Common Core: Major Standards:
S-ID.C.7

Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S-ID.C.8

Interpret linear models. Compute (using technology) and interpret the correlation coefficient of a linear fit.

S-ID.C.9

Interpret linear models​. Distinguish between correlation and causation.

S-IC.B.4

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S-IC.B.5

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Common Core: Supporting Standards:
S-ID.B.5

Summarize, represent, and interpret data on two categorical and quantitative variables.  Summarize categorical data 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.

S-ID.B.6

Summarize, represent, and interpret data on two categorical and quantitative variables.  Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S-ID.B.6a

Summarize, represent, and interpret data on two categorical and quantitative variables. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.  Clarification: includes the use of the regression capabilities of the calculator

S-IC.A.1

Understand and evaluate random processes underlying statistical experiments.  Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S-IC.A.2

Understand and evaluate random processes underlying statistical experiments.  Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Common Core: Additional Standards:
S-ID.A.4

Summarize, represent, and interpret data on a single count or measurement variable. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Evidence of Understanding

  • interpret bivariate data from a scatter plot
    • describe the relationship between variables for the graph of a scatter plot
    • describe how several points in a data set are related
    • interpret a single data point and explain its relationship to the data set
      • identify an outlier in the data set and justify reasoning
    • create a scatter plot and describe the correlation between data points in a set
    • distinguish correlation and causation
  • use the function of best fit to interpret and compare data points of a scatterplot
    • explain what the function of best fit represents for a scatter plot
    • use the function of best fit to interpret or compare points in the scatterplot
    • calculate the function of best fit (linear, quadratic, or exponential) to a given set of data
      • use technology (eg. graphing calculator) to determine the function of best fit based on the entire set of coordinates
      • use algebra (eg. a system of equations for a quadratic or exponential model) to determine the function of best fit based on estimated coordinates of the function
    • determine if and how well a given model fits the data based on the amount of correlation (strong, weak, or no correlation, positive or negative correlation), for a given data set
      • compute and interpret the correlation coefficient
    • use a fitted function to predict and justify other possible data points or solve situations
      • interpolate or extrapolate and describe possible problems for each estimation method
    • use a variety of methods to draw the function of best fit for a data set and justify each approach
      • Examples:  equal number of data points on each side of the function, informally “measure” the distance of points from the function, function passes through the most points in the set, use technology to graph the function

Develop conceptual understanding:

bivariate, scatter plot, function of best fit, correlation, correlation coefficient, causation, interpolate, extrapolate

Supporting terms to communicate:

statistics, data point, data set, independent, dependent, domain, range, random, sample, categorized, summarized, discrete, continuous
Core Resource

A core resource supports multiple days of instruction.

Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.