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

MA19.GDA.7

Use mathematical and statistical reasoning with quantitative data, both univariate data (set of values) and bivariate data (set of pairs of values) that suggest a linear association, in order to draw conclusions and assess risk.

COS Examples

Example: Estimate the typical age at which a lung cancer patient is diagnosed, and estimate how the typical age differs depending on the number of cigarettes smoked per day.

Unpacked Content

Knowledge

Students know:
  • Patterns found on scatter plots of bivariate data.
  • Strategies for determining slope and intercepts of a linear model.
  • Strategies for informally fitting straight lines to bivariate data with a linear relationship.
  • Methods for finding the distance between two points on a coordinate plane and between a point and a line.

Skills

Students are able to:
  • Construct a scatter plot to represent a set of bivariate data.
  • Use mathematical vocabulary to describe and interpret patterns in bivariate data.
  • Use logical reasoning and appropriate strategies to draw a straight line to fit data that suggest a linear association.
  • Use mathematical vocabulary, logical reasoning, and closeness of data points to a line to judge the fit of the line to the data.
  • Find a central value using mean, median and mode.
  • Find how spread out the univariate data is using range, quartiles and standard deviation.
  • Make plots like Bar Graphs, Pie Charts and Histograms.

Understanding

Students understand that:
  • Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated,
  • When visual examination of a scatter plot suggests a linear association in the data, fitting a straight line to the data can aid in interpretation and prediction.
  • Modeling bivariate data with scatter plots and fitting a straight line to the data can aid in interpretation of the data and predictions about unobserved data.
  • A set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
  • Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated.
  • Statistical measures of center and variability that describe data sets can be used to compare data sets and answer questions.

Vocabulary

  • Mathematical reasoning
  • Statistical reasoning
  • Univariate data
  • bivariate data
  • quantitative data
  • linear association
  • Scatter plots
  • linear model
  • Slope
  • bar graphs, Pie graphs, Histograms
  • Mean, median, mode
  • Standard deviation
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