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STANDARDS

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US-VA

Math

Virginia Math

Probability and Statistics: Descriptive Statistics

PS.DS.1

The student will represent and analyze data visualizations of univariate quantitative data, including dot plots, stemplots, boxplots, cumulative frequency graphs, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers, within the context of a problem.

PS.DS.1.a

Create and interpret graphical displays of data, including dot plots, stemplots, boxplots, cumulative frequency graphs, and histograms, using appropriate technology.

PS.DS.1.b

Examine the graphs within the context of the problem by analyzing:

PS.DS.1.b.i

shape;
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PS.DS.1.b.ii

measures of center;

PS.DS.1.b.iii

spread; and
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PS.DS.1.b.iv

unusual features of the data (e.g., outliers, clusters, gaps).
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PS.DS.2

The student will represent and analyze numerical characteristics of univariate quantitative data sets to describe patterns and departures from patterns within the context of a problem.

PS.DS.2.a

Interpret measures of central tendency: mean, median, and mode.

PS.DS.2.b

Interpret measures of spread: range, interquartile range, variance, and standard deviation.

PS.DS.2.c

Identify possible outliers, using an algorithm.
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PS.DS.2.d

Investigate and explain the influence of outliers on a univariate data set.
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PS.DS.2.e

Investigate and explain ways in which standard deviation addresses variability by examining the formula for standard deviation.
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PS.DS.3

The student will represent, compare, and analyze distributions of two or more univariate quantitative data sets, numerically and graphically.

PS.DS.3.a

Create graphical displays of data, including back-to-back stemplots, parallel dot plots, parallel boxplots, and histograms, using appropriate technology.
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PS.DS.3.b

Compare and contrast two or more univariate data sets, numerically and graphically, within the context of a problem by analyzing:

PS.DS.3.b.i

shape;
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PS.DS.3.b.ii

measures of center;
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PS.DS.3.b.iii

measures of spread; and

PS.DS.3.b.iv

unusual features of the data (e.g., clusters, gaps, outliers).
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PS.DS.4

The student will represent and analyze categorical data, using two-way tables and other graphical displays, to describe patterns and relationships.

PS.DS.4.a

Create and interpret graphical displays of univariate categorical data, including bar graphs within the context of the problem, using appropriate technology.
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PS.DS.4.b

Create and interpret graphical displays comparing distributions of two or more univariate categorical data sets including segmented and side-by-side bar graphs within the context of the problem, using appropriate technology.
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PS.DS.4.c

Generate and interpret a two-way table as a summary of the information obtained from two categorical variables.
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PS.DS.4.d

Calculate and interpret marginal, relative, and conditional frequencies to analyze data in a two-way table within the context of a problem.
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PS.DS.5

The student will represent and analyze quantitative bivariate data with scatterplots to identify and describe the relationship between two variables.

PS.DS.5.a

Create scatterplots, using appropriate technology.
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PS.DS.5.b

Examine and interpret scatterplots in the context of the problem by analyzing:

PS.DS.5.b.i

the form of relationship for linear and nonlinear trends;
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PS.DS.5.b.ii

the direction of the relationship for positive, negative, or no association;
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PS.DS.5.b.iii

the strength of the relationship such as strong, moderate, or weak; and
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PS.DS.5.b.iv

the presence of unusual features within the data (e.g., clusters, gaps, influential points, outliers).
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PS.DS.6

The student will create and interpret a linear model using the least squares regression method to assess the relationship between two quantitative variables.

PS.DS.6.a

Create the least squares regression model using technology to interpret the contextual meaning of the slope and 𝑦-intercept.
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PS.DS.6.b

Using technology, calculate and interpret the correlation coefficient, 𝑟, within the context of a problem.
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PS.DS.6.c

Using technology, calculate and interpret the coefficient of determination, 𝑟², within the context of a problem.
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PS.DS.6.d

Use regression lines to make predictions, and identify the limitations of the predictions, such as extrapolation.
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PS.DS.6.e

Calculate and interpret a residual to understand the error of a prediction.
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PS.DS.6.f

Using technology, calculate and interpret the standard deviation of the residuals, 𝑠.
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