Classroom Resource

Measures of Center | Against All Odds: Unit 4

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Discover how calculating median and mean reveal different ways to describe a center of distribution in this 9-minute video from the Against All Odds statistics series. This video resource will examine differences in comparable wages for men and women to see practical applications of statistics and data visualization.

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.A2.25

From a normal distribution, use technology to find the mean and standard deviation and estimate population percentages by applying the empirical rule.

Unpacked Content

UP:MA19.A2.25

Vocabulary

  • Normal distribution
  • Population Percentages
  • Empirical Rule
  • Normal curve
  • Mean
  • Standard deviation

Knowledge

Students know:
From a normal distribution,
  • Techniques to find the mean and standard deviation of data sets using technology.
  • Techniques to use calculators, spreadsheets, and standard normal distribution tables to estimate areas under the normal curve.

Skills

Students are able to:
  • From a normal distribution, accurately find the mean and standard deviation of data sets using technology.
  • Make reasonable estimates of population percentages from a normal distribution.
  • Read and use normal distribution tables and use calculators and spreadsheets to accurately estimate the areas under a normal curve.

Understanding

Students understand that:
Under appropriate conditions,
  • The mean and standard deviation of a data set can be used to fit the data set to a normal distribution.
  • Population percentages can be estimated by areas under the normal curve using calculators, spreadsheets, and standard normal distribution tables.
Link to Resource
https://aptv.pbslearningmedia.org/resource/6e723a01-3442-4384-8afc-0eea0adaae1c…

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

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