Big Idea:

Big idea 3

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

1 week

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.

  • Studying Samples
    Connect what students know about reading and creating frequency distributions, calculating mean and standard deviation for a set of data, and calculating probabilities of events occurring to determine if a sample and control group are statistically significantly different.
    Resource:
    Studying Samples

    Connect what students know about reading and creating frequency distributions, calculating mean and standard deviation for a set of data, and calculating probabilities of events occurring to determine if a sample and control group are statistically significantly different.

    This Core Resource does not yet emphasis the distinction between joint, marginal, and conditional relative frequencies.

    All Resources From:
Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!
    Instructional Routine: Connecting Representations
    These tasks are embedded within the instructional routine called Connecting Representations.
    • Normal Distribution Curves
      Students will use the mean and standard deviation of a data set to fit it to a normal distribution thereby getting a better understanding of the structure of graphs and the areas highlighted for Normal Distribution Curves.
      Resource:
      Normal Distribution Curves

      Students will use the mean and standard deviation of a data set to fit it to a normal distribution thereby getting a better understanding of the structure of graphs and the areas highlighted for Normal Distribution Curves.

      All Resources From: