Access Point #: MAFS.912.S-ID.1.AP.2d Archived Access Point

Compare two or more different data sets using the center and spread of each.

Clarifications:

Essential Understandings

Concrete:

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  • Back to Back Stem Plots:
    Amount of money carried by teenage boys and girls:

    Data for amount of money carried by teenage boys and girls.
  • Find the mean.
  • Mean: boys $44.43, girls $34.93
  • Find the median.
  • Median: boys $42, girls $36
  • Find the interquartile range (IQR).
  • IQR = Q3 – Q1
  • IQR: boys $59 - $34 = $25, girls $44 - $28 = $16
  • Find the standard deviation.
  • Standard Deviation: boys $18.43, girls $10.47.
  • Center: On average, the boys carry more money than the girls.
  • Spread: The amount of money carried by boys is more dispersed than the amount of money carried by girls.
  • Double Bar Charts:

    Data for pretest and post test scores for Whitney of 75 then 90, Alex of 55 then 55, Erica of 80 then 95, and Kacie of 60 then 70.

    Bar Chart showing data for pretest and post test scores for Whitney of 75 then 90, Alex of 55 then 55, Erica of 80 then 95, and Kacie of 60 then 70.
  • Find the mean.
  • Mean: Pretest 67.5, Post-test 77.5
  • Find the median.
  • Median: Pretest 67.5, Post-test 80
  • Find the interquartile range (IQR).
  • IQR = Q3 – Q1
  • IQR: Pretest 77.5 – 57.5 = 20, Post-test 92.5 – 62.5 = 30
  • Find the standard deviation.
  • Standard Deviation: Pretest 11.9, Post-test 18.48.
  • Center: On average, students scored higher on the post-test than the pretest.
  • Spread: The post-test scores were more dispersed than the pretest scores.
Representation:
  • Understand the following concepts and vocabulary: center, spread, data points, median, mean, quartile, 5 number summary (minimum, Q1, median, Q3, maximum), maximum, minimum, lower bound, upper bound, standard deviation and interquartile range.
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  • Use graphs or graphic organizers to compare the measures of central tendency of two different data sets.
  • Identify the same measure of central tendency in two different data sets (e.g., the mean in one data set and the mean in another data set).
  • Read and interpret each display of given data (e.g., bell curve, scatter plot, box plot, stem plot) to draw inferences about the data.
  • When comparing two standard deviations, understand that the larger standard deviation indicates more variability (spread). For example, in the stem plot, the boys’ standard deviation of $18.43 versus the girls’ standard deviation of $10.47 means that the amount of money carried by teenage boys is dispersed further from the mean than the amount of money carried by girls.
General Information

Number: MAFS.912.S-ID.1.AP.2d

Category: Access Points

Date Adopted or Revised: 07/14

Cluster: Summarize, represent, and interpret data on a single count or measurement variable. (Algebra 1 - Additional Cluster) (Algebra 2 - Additional Cluster) :  Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

This access point is part of these courses.