Classroom Resource

Understanding a Crowd's Predictive Ability | Prediction by the Numbers

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Examine a mathematical theory known as the “wisdom of crowds,” which holds that a crowd’s predictive ability is greater than that of an individual, in this video from NOVA: Prediction by the Numbers. Sir Francis Galton documented this phenomenon after witnessing a weight-guessing contest more than a hundred years ago at a fair. Statistician Talithia Williams tests Galton’s theory with modern-day fairgoers, asking them to guess the number of jelly beans in a jar. Use this resource to stimulate thinking and questions about the use of statistics in everyday life and to make evidence-based claims about predictive ability.

Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.10

Use statistics appropriate to the shape of the data distribution to compare and contrast two or more data sets, utilizing the mean and median for center and the interquartile range and standard deviation for variability.

Unpacked Content

UP:MA19.GDA.10

Vocabulary

  • Center
  • Median
  • Mean
  • Spread
  • Interquartile range
  • Standard deviation
  • Absolute mean deviation

Knowledge

Students know:
  • Techniques to calculate the center and spread of data sets.
  • Techniques to calculate the mean absolute deviation and standard deviation.
  • Methods to compare data sets based on measures of center (median, mean) and spread (interquartile range and standard deviation) of the data sets.

Skills

Students are able to:
  • Accurately find the center (median and mean) and spread (interquartile range and standard deviation) of data sets.
  • -Present viable arguments and critique arguments of others from the comparison of the center and spread of multiple data sets.
  • Explain their reasoning on how standard deviation develops from the mean absolute deviation.

Understanding

Students understand that:
  • Multiple data sets can be compared by making observations about the center and spread of the data.
  • The center and spread of multiple data sets are used to justify comparisons of the data.
  • Both the mean and the median are used to calculate the mean absolute and standard deviations
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.11

Interpret differences in shape, center, and spread in the context of data sets, accounting for possible effects of extreme data points (outliers) on mean and standard deviation.

Unpacked Content

UP:MA19.GDA.11

Vocabulary

  • Outliers
  • Center
  • Shape
  • Spread
  • Mean
  • Standard deviation

Knowledge

Students know:

  • Techniques to calculate the center and spread of data sets.
  • Methods to compare attributes (e.g. shape, median, mean, interquartile range, and standard deviation) of the data sets.
  • Methods to identify outliers.

Skills

Students are able to:

  • Accurately identify differences in shape, center, and spread when comparing two or more data sets.
  • Accurately identify outliers for the mean and standard deviation.
  • Explain, with justification, why there are differences in the shape, center, and spread of data sets.

Understanding

Students understand that:

  • Differences in the shape, center, and spread of data sets can result from various causes, including outliers and clustering.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.26

Describe the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Unpacked Content

UP:MA19.A2.26

Vocabulary

  • Sample surveys
  • Experiments
  • Observational studies
  • Randomization

Knowledge

Students know:
  • Key components of sample surveys, experiments, and observational studies.
  • Procedures for selecting random samples.

Skills

Students are able to:
  • Use key characteristics of sample surveys, experiments, and observational studies to select the appropriate technique for a particular statistical investigation.

Understanding

Students understand that:
  • Sample surveys, experiments, and observational studies may be used to make inferences made about the population.
  • Randomization is used to reduce bias in statistical procedures.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.27

Distinguish between a statistic and a parameter and use statistical processes to make inferences about population parameters based on statistics from random samples from that population.

Unpacked Content

UP:MA19.A2.27

Vocabulary

  • Population parameters
  • Random samples
  • Inferences

Knowledge

Students know:
  • Techniques for selecting random samples from a population.

Skills

Students are able to:
  • Accurately compute the statistics needed.
  • Recognize if a sample is random.
  • Reach accurate conclusions regarding the population from the sample.

Understanding

Students understand that:
  • Statistics generated from an appropriate sample are used to make inferences about the population.
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.33

Use data from a randomized experiment to compare two treatments; limit to informal use of simulations to decide if an observed difference in the responses of the two treatment groups is unlikely to have occurred due to randomization alone, thus implying that the difference between the treatment groups is meaningful.

Unpacked Content

UP:MA19.A2.33

Vocabulary

  • Randomized experiment
  • Significant
  • Parameters

Knowledge

Students know:
  • Techniques for conducting randomized experiments.
  • Techniques for conducting simulations of randomized experiment situations.

Skills

Students are able to:
  • Design and conduct randomized experiments with two treatments.
  • Draw conclusions from comparisons of the data of the randomized experiment.
  • Design, conduct, and use the results from simulations of a randomized experiment situation to evaluate the significance of the identified differences.

Understanding

Students understand that:
  • Differences of two treatments can be justified by a significant difference of parameters from a randomized experiment.
  • Statistical analysis and data displays often reveal patterns in data or populations, enabling predictions.
Link to Resource
https://aptv.pbslearningmedia.org/resource/nvpn-sci-crowds/understanding-a-crow…

CR Resource Type

Audio/Video

Resource Provider

PBS
Accessibility

Accessibility

Video resources: includes closed captioning or subtitles
License

License Type

Custom

Custom License Type (URL)

https://aptv.pbslearningmedia.org/help/terms-of-use/#.YD-bCNhKiUk

Approved Date

ALSDE LOGO

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