Topic: Statistics and Probability 
Common Core Mathematics 68 
 Cluster Develop understanding of statistical variability. 
  Grade 6 
   6.SP.1.  Recognize a statistical question as one that anticipates variability in
the data related to the question and accounts for it in the answers. For
example, “How old am I?” is not a statistical question, but “How old are the
students in my school?” is a statistical question because one anticipates
variability in students’ ages. 
   6.SP.2.  Understand that a set of data collected to answer a statistical question
has a distribution which can be described by its center, spread, and
overall shape. 
   6.SP.3.  Recognize that a measure of center for a numerical data set
summarizes all of its values with a single number, while a measure of
variation describes how its values vary with a single number. 
 Cluster Summarize and describe distributions. 
  Grade 6 
   6.SP.4.  Display numerical data in plots on a number line, including dot plots,
histograms, and box plots. 
   6.SP.5.  Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation,
including how it was measured and its units of measurement.
c. Giving quantitative measures of center (median and/or mean) and
variability (interquartile range and/or mean absolute deviation), as
well as describing any overall pattern and any striking deviations
from the overall pattern with reference to the context in which the
data were gathered.
d. Relating the choice of measures of center and variability to the
shape of the data distribution and the context in which the data
were gathered.

 Cluster Use random sampling to draw inferences about a population. 
  Grade 7 
   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. 
   7.SP.2.  Use data from a random sample to draw inferences about a population
with an unknown characteristic of interest. 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. 
 Cluster Draw informal comparative inferences about two populations. 
  Grade 7 
   7.SP.3.  Informally assess the degree of visual overlap of two numerical
data distributions with similar variabilities, 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 heights is
noticeable. 
   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 seventhgrade science book are generally longer than the words in a
chapter of a fourthgrade science book. 
 Cluster Investigate chance processes and develop, use, and evaluate
probability models. 
  Grade 7 
   7.SP.5.  Understand that the probability of a chance event is a number
between 0 and 1 that expresses the likelihood of the event occurring.
Larger numbers indicate greater likelihood. A probability near 0
indicates an unlikely event, a probability around 1/2 indicates an event
that is neither unlikely nor likely, and a probability near 1 indicates a
likely event. 
   7.SP.6.  Approximate the probability of a chance event by collecting data on
the chance process that produces it and observing its longrun relative
frequency, and predict the approximate relative frequency given the
probability. For example, when rolling a number cube 600 times, predict
that a 3 or 6 would be rolled roughly 200 times, but probably not exactly
200 times. 
   7.SP.7.  Develop a probability model and use it to find probabilities of events.
Compare probabilities from a model to observed frequencies; if the
agreement is not good, explain possible sources of the discrepancy. 
   7.SP.7.a.  Develop a uniform probability model by assigning equal
probability to all outcomes, and use the model to determine
probabilities of events. For example, if a student is selected at
random from a class, find the probability that Jane will be selected
and the probability that a girl will be selected. 
   7.SP.7.b.  Develop a probability model (which may not be uniform) by
observing frequencies in data generated from a chance process.
For example, find the approximate probability that a spinning penny
will land heads up or that a tossed paper cup will land openend
down. Do the outcomes for the spinning penny appear to be equally
likely based on the observed frequencies? 
   7.SP.8.  Find probabilities of compound events using organized lists, tables,
tree diagrams, and simulation. 
   7.SP.8.a.  Understand that, just as with simple events, the probability of a
compound event is the fraction of outcomes in the sample space
for which the compound event occurs. 
   7.SP.8.b.  Represent sample spaces for compound events using methods
such as organized lists, tables and tree diagrams. For an event
described in everyday language (e.g., “rolling double sixes”),
identify the outcomes in the sample space which compose the
event. 
   7.SP.8.c.  Design and use a simulation to generate frequencies for
compound events. For example, use random digits as a simulation
tool to approximate the answer to the question: If 40% of donors
have type A blood, what is the probability that it will take at least 4
donors to find one with type A blood? 
 Cluster Investigate patterns of association in bivariate data. 
  Grade 8 
   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. 
   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. 
   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 twoway table. Construct and interpret a twoway 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? 