

Unit 4 Statistics Algebra I 

Unit
Length and Description: 25
days Experience with descriptive statistics began
as early as Grade 6. Students were expected to display numerical data and
summarize it using measures of center and variability. By the end of middle
school they were creating scatterplots and recognizing linear trends in
data. This unit builds upon that prior experience, providing students with
more formal means of assessing how a model fits data. Students use regression
techniques to describe approximately linear relationships between quantities.
They use graphical representations and knowledge of the context to make
judgments about the appropriateness of linear models. With linear models,
they look at residuals to analyze the goodness of fit. (Mathematics Appendix A, p.22) ·
Summarize, represent,
and interpret data on a single count or measurement variable; choose a
summary statistic appropriate to the characteristics of data distribution. ·
Summarize, represent,
and interpret data on two categorical quantitative variables; use linear
functions to model the relationship between two numerical variables and
assess how well the line of best fit models the data using residuals. ·
Interpret linear
models; focus on computation and interpretation of the correlation
coefficient as a measure of the of how well the data fit the relationship ·
Distinction between a
statistical relationship and a causeandeffect relationship. 

Standards: SID.A.1 Represent data with plots on the real number
line (dot plots, histograms, and box plots). SID.A.2 Use statistics appropriate to the shape of
the data distribution to compare center (median, mean) and spread
(interquartile range, standard deviation) of two or more different data sets. SID.A.3 Interpret differences in shape, center, and
spread in the context of the data sets, accounting for possible effects of
extreme data points (outliers). SID.B.5 Summarize categorical data for two
categories in twoway frequency tables. Interpret relative frequencies in the
context of the data (including joint, marginal, and conditional relative
frequencies). Recognize possible associations and trends in the data. SID.B.6 Represent data on two quantitative
variables on a scatter plot, and describe how the variables are related.
SID.C.7 Interpret the slope (rate of change) and
the intercept (constant term) of a linear model in the context of the data. SID.C.8 Compute (using technology) and interpret
the correlation coefficient of a linear fit. SID.C.9 Distinguish between correlation and causation. Focus Standards of
Mathematical Practice: MP.1 Make sense of problems and persevere in
solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the
reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated
reasoning. Instructional Outcomes: Full Development
of the Major Clusters, Supporting Clusters, Additional Clusters and
Mathematical Practices for this unit could include the following
instructional outcomes: SID.A.1 ·
I
can represent data with plots on the real number line using various display
types by creating dot plots, histograms and box plots SID.A.2 ·
I
can choose the appropriate measure for center (mean, median) and spread
(interquartile range, standard deviation) based on the shape of a data
distribution ·
I
can use appropriate statistics for center and spread to compare two or more
data sets SID.A.3 ·
I
can define “the context of data sets” as measuring the specific nature of the
attributes under investigation ·
I
can interpret differences in shape, center and spread in the context of data
sets ·
I
can describe the possible effects the presence of outliers in a set of data
can have on shape, center, and spread in the context of the data sets SID.B.5 ·
I
can recognize the differences between joint, marginal and conditional
relative frequencies ·
I
can calculate relative frequencies including joint, marginal and conditional
relative frequencies ·
I
can summarize categorical data for two categories in twoway frequency tables
·
I
can interpret relative frequencies in the context of the data ·
I
can recognize possible associations and trends in the data SID.B.6 ·
I
can represent data on a scatter plot (2 quantitative variables) ·
I
can fit a given function class (e.g. linear, exponential) to data ·
I
can, using given scatter plot data represented on the coordinate plane,
informally describe how the two quantitative variables are related ·
I
can determine which function best models scatter plot data represented on the
coordinate plane, and describe how the two quantitative variables are related
·
I
can use functions fitted to data to solve problems in the context of the data
·
I
can represent the residuals from a function and the data set it models
numerically and graphically ·
I
can informally assess the fit of a function by analyzing residuals from the
residual plot ·
I
can fit a linear function for a scatter plot that suggests a linear
association SID.C.7 ·
I
can interpret the slope (rate of change) and model the intercept (constant
term) of a linear model in the context of the data SID.C.8 ·
I
can compute (using technology) the correlation coefficient of a linear fit ·
I
can define the correlation coefficient ·
I
can interpret the correlation coefficient of a linear fit as a measure of how
well the data fit the relationship SID.C.9 ·
I
can define positive, negative, and no correlation and explain why correlation
does not imply causation ·
I
can define causation ·
I can distinguish between correlation and
causation 

Enduring
Understandings: ·
The way
that data is collected, organized, and displayed influences interpretation. ·
Describing
center, spread, and shape is essential analysis of both univariate and
bivariate data. ·
Mathematical
models are used to predict and make inferences about data. ·
Mathematics
can be used to solve real world problems and can be used to communicate
solutions. 
Essential
Questions: ·
How
do various representations of data lead to different interpretations of the
data? ·
How
are center and spread of data sets described and compared? ·
What
information is appropriate to interpret from a databased model? ·
How
can mathematical representations be used to communicate information
effectively? 
