Trajectory: Data Analysis
Grade 7
Sampling and
Design
Formulate
Questions that
can be
addressed
with data and
collect,
organize, and
display
relevant data
to answer
questions
Data
Distributions
Select and use
statistical
methods to
analyze data
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Grade 8
7.SP. 1 Understand that statistics can be
used to gain information about a population
by examining a sample of the population;
generalizations about a population from a
sample are valid only if the sample is
representative of that population.
Understand that random sampling tends to
produce representative samples and support
valid inferences.
Algebra I
Algebra II and Beyond
S.ID.1 Represent data with plots on the real
number line (dot plots, histograms, and box
plots).
S.IC.3 Recognize the purposes of and
differences among sample surveys,
experiments, and observational studies;
explain how randomization relates to each.
7.SP.2 Use data from a random sample to
draw inferences about a population.
Generate multiple samples (or simulated
samples) of the same size to gauge the
variation in estimates or predictions. For
example, estimate the mean word length in
a book by randomly sampling words from
the book; predict the winner of a school
election based on randomly sampled survey
data. Gauge how far off the estimate or
prediction might be.
7.SP.3 Informally assess the degree of visual
overlap of two numerical data distributions
with similar variabilities (variation),
measuring the difference between the
centers by expressing it as a multiple of a
measure of variability. For example, the
mean height of players on the basketball
team is 10 cm greater than the mean height
of players on the soccer team, about twice
the variability (mean absolute deviation) on
either team; on a dot plot, the separation
between the two distributions of height is
noticeable.
8.SP.1 Construct and interpret scatter plots for
bivariate measurement data to investigate
patterns of association between two quantities.
Describe patterns such as clustering, outliers,
positive or negative association, linear
association, and nonlinear association.
S.ID.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.
8.SP.2 Know that straight lines are widely used to
model relationships between two quantitative
variables. For scatter plots that suggest a
linear association, informally fit a straight line,
and informally assess the model fit by judging
the closeness of the data points to the line.
S.ID.5 Summarize categorical data for two
categories in two-way 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.
8.SP.3 Use the equation of a linear model to
solve problems in the context of bivariate
measurement data, interpreting the slope and
intercept. For example, in a linear model for a
biology experiment, interpret a slope of 1.5
cm/hr as meaning that an additional hour of
sunlight each day is associated with an additional
1.5 cm in mature plant height.
8.SP.4 Understand that patterns of association
can also be seen in bivariate categorical data by
displaying frequencies and relative frequencies
in a two-way table. Construct and interpret a
two-way table summarizing data on two
categorical variables collected from the same
subjects. Use relative frequencies calculated for
rows or columns to describe possible association
between the two variables. For example, collect
data from students in your class on whether or
not they have a curfew on school nights and
whether or not they have assigned chores at
home. Is there evidence that those who have a
curfew also tend to have chores?
Interpret
Results
Develop and
evaluate
inferences and
predictions
based on data
7.SP.4 Use measures of center and measures
of variability for numerical data from
random samples to draw informal
comparative inferences about two
populations. For example, decide whether
the words in a chapter of a seventh-grade
science book are generally longer than the
words in a chapter of a fourth-grade science
book.
S.ID.6 Represent data on two quantitative
variables on a scatter plot, and describe how
the variables are related.
a. Fit a function to the data; use functions
fitted to data to solve problems in the
context of the data. Use given functions or
choose a function suggested by the context.
Emphasize linear and exponential models.
b. Informally assess the fit of a function by
plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that
suggests a linear association.
S.ID.7 Interpret the slope (rate of change) and
the intercept (constant term) of a linear model
in the context of the data.
S.ID.8 Compute (using technology) and
interpret the correlation coefficient of a linear
fit.
S.ID.9 Distinguish between correlation and
causation.
S.ID.3 Interpret differences in shape, center,
and spread in the context of the data sets,
accounting for possible effects of extreme data
points (outliers).
S.ID. 4 Use the mean and standard deviation
of a data set to fit it to a normal distribution
and to estimate population percentages.
Recognize that there are data sets for which
such a procedure is not appropriate.
Use calculators, spreadsheets, and tables to
estimate areas under the normal curve.
S.IC.1 Understand statistics as a process for
making inferences about population
parameters based on a random sample from
that population.
S.IC.2. Decide if a specified model is
consistent with results from a given datagenerating process, e.g., using simulation. For
example, a model says a spinning coin falls
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heads up with probability 0.5. Would a result
of 5 tails in a row cause you to question the
model?
S.IC.4 Use data from a sample survey to
estimate a population mean or proportion;
develop a margin of error through the use of
simulation models for random sampling.
S.IC.5 Use data from a randomized
experiment to compare two treatments; use
simulations to decide if differences between
parameters are significant.
S.IC.6 Evaluate reports based on data.
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