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 3

Statistical data from random processes can be predicted using probability calculations.

1 week
See Standards
Common Core: Major Standards:
S-IC.B.3

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

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.

S-IC.B.6

Make inferences and justifying conclusions from sample surveys, experiments, and observational studies. Evaluate reports based on data.

Common Core: Supporting Standards:
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.

Evidence of Understanding

  • predict the theoretical probability of an event occurring based on a sample
    • construct two way frequency tables and summarize data for each category
      • identify joint,marginal and conditional relative frequencies
      • interpret relative frequencies in context and describe possible trends
    • use the mean and standard deviation of a data set to fit it to a normal distribution
      • use technology to calculate the mean and standard deviation of a data set
      • analyze the variables, chart, or table of a data set and explain whether or not it is normally distributed
    • describe the differences between a theoretical statistical distribution and the experimental distribution.
    • determine, using a simulation, if a given set of experimental results are consistent with the theoretical results.
  • compare two data sets resulting from variation in the same set of parameters to determine if change in those parameters is statistically significant. For example: Compare data sets from different groups in an experiment to see if the resulting data is statistically different.
    • construct two way frequency tables and summarize data for each category
      • identify joint,marginal and conditional relative frequencies
      • interpret relative frequencies in context and describe possible trends
    • use simulations and experiments to generate two or more data sets
    • recognize the similarities and differences between two data sets by examining different representations of the two data sets
    • based on examining a simulation, determine the probability that the variation between two data sets is statistically significant (see this example)
  • communicate statistical information in a variety of different formats and representations
    • describe how different representations (graphs, charts, tables, formulas) can be used to communicate and potentially miscommunicate different meaning about statistics
    • choose representations for communicating statistics based on the appropriateness of these representations

Develop conceptual understanding:

frequency, joint, marginal, conditional, relative, standard deviation, theoretical, empirical, experimental, statistically significant

Supporting terms to communicate:

statistics, univariate, bivariate, measures of center, outlier, density, variability, standard deviation, distribution, spread, correlation, causation, interpolate, extrapolate, 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.