Download Statistics and Probability 8.SP.1

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Pomona Unified Math News
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Domain: 8 Grade Statistics and Probability (SP)
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.
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Suggested Standards for Mathematical
Practice (MP):
MP 2 Reason abstractly and quantitatively:
As students work towards analyzing sets of
data, they must reason quantitatively by using
data to determine association. MP.4 Model
with mathematics: Modeling real life
scenarios and problems using statistics can
allow students to draw connections with
mathematics. MP.5 Use appropriate tools
strategically: Students should be given access
to work with and use statistical software and
calculators to analyze statistical data. MP.6
Attend to precision: When analyzing data,
students should be precise with their
calculations as well as their vocabulary. MP.7
Look for and make use of structure:
Working with and analyzing data requires
students to look for patterns that exist between
multiply variables in data sets.
Vocabulary:
(Note: vocabulary will be taught in the context
of the lesson, not before or separate from the
lesson.)
correlation/association: any relationship
between two measured quantities that renders
them statistically dependent
bivariate data: Data for two variables (usually
two types of related data).
Example: Ice cream sales versus the
temperature on that day. The two variables are
Ice Cream Sales and Temperature.
(If you have only one set of data, such as just
Temperature, it is called "Univariate Data")
Temperature and Ice Cream Sales
Scatter plot: a graphic tool used to display the
relationship between two quantitative variables.
Each dot on the scatterplot represents one
observation from a data set. The position of the
dot on the scatterplot represents its X and Y
values.
Consider the example below. The table shows
the height and the weight of five starters on a
high school basketball team. Then, the same
data are displayed in a scatterplot.
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Adapted from Georgia Math Grade 8 flip
book and www.mathisfun.com
Height (in.)
67
72
77
74
69
Weight (lb)
155
220
240
195
175
!
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Pomona Unified Math News
th
Domain: 8 Grade Statistics and Probability (SP)
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.
Each player in the table is represented by a dot
on the scatterplot. The first dot, for example,
represents the shortest, lightest player. From
the scale on the X axis, you see that the shortest
player is 67 inches tall; and from the scale on
the Y axis, you see that he/she weighs 155
pounds. In a similar way, you can read the
height and weight of every other player
represented on the scatterplot.
more independent variables and, thus, can be
computed as the linear function of the
independent variable(s).
Curvature: a bivariate relationship that creates
a scatterplot with a curvilinear relationship.
Weight and Height of Boys High School
Basketball Players
Connections: r 8.NS.1
Scatterplots are helpful in understanding
patterns in bivariate data . For example, the
above scatterplot shows that the relationship
between height and weight is linear and has a
positive slope.
This Cluster is connected to Grade 8 Critical
Area of Focus #1: Formulating and reasoning
about expressions and equations, including
modeling an association in bivariate data with a
linear equation, and solving linear equations
and systems of linear equations. (MP 4: model
with mathematics.)
Outlier: a data point that diverges greatly from
the overall pattern of data.
Explanations and Examples:
Linearity: Situation where a dependent
variable has a liner relationship with one or
Students analyze scatter plots to determine
positive and negative associations, the degree
Bivariate data refers to two variable data, one
to be graphed on the x-axis and the other on the
y-axis. Students represent measurement
(numerical) data on a scatter plot, recognizing
patterns of association. These patterns may be
linear (positive, negative or no association) or
non-linear.
Students build on their previous knowledge of
scatter plots to examine relationships between
variables.
!
!
Pomona Unified Math News
th
Domain: 8 Grade Statistics and Probability (SP)
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.
of association, and type of association.
Students examine outliers to determine if data
points are valid or represent a recording or
measurement error. Students can use tools such
as those at the National Center for Educational
Statistics to create a graph or generate data sets.
Example 1:
Example 2:
Data from a local fast food restaurant is
provided showing the number of staff members
and the average time for filling an order.
Describe the association between the number
of staff and the average time for filling an
order.
Data for 10 students‘ Math and Science scores
are provided in the chart. Describe the association between the Math and Science scores.
Sample Answer:
Sample Answer:
The score difference between Math and
Science are very close. I would posit that there
is a direct positive correlation between Math
scores and Science scores. That is, the better a
student is doing in math, the better they are
scoring in science. There is one possible outlier
or student that does not fit that statement.
Student number two scores really well in
science but doesn’t score that well in math. To
see this better, let’s look at a graph of the data.
Math and Science Scores Science Scores
Average time (sec.) to fill
an order
100 80 60 40 20 0 0 20 40 60 Math Scores
80 100 The association that I notice is that every time
the number of staff members increases the
average time in seconds to fill an order
decreases. When there are 3 staff members the
average time is 180 seconds while when there
are 8 staff members the time in seconds
decreases to an average of 84 seconds. This
means that every time a staff member is added
to an order, the order completion becomes
more efficient.
Number of Staff Members and Average time to 7ill order 200 150 100 50 0 0 2 4 6 8 10 Number of Staff Members
Example 3:
The chart below lists the life expectancy in
years for people in the United States from 1970
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Pomona Unified Math News
th
Domain: 8 Grade Statistics and Probability (SP)
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.
to 2005 in five-year increments. What would
you expect the life expectancy of a person in
the United States to be in 2010, 2015, and 2020
based upon this data? Explain how you
determined your values.
now ready to study bivariate data.
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Sample Answer:
The average life expectancy in years is
increasing every five years. Every five years,
the increase is an increase of life in years on
average of +1 year.
72.6 – 70.8 = 1.8
73.7 – 72.6 = 1.1
74.7 – 73.7 = 1
75.4 – 74.7 = .7
75.8 – 75.4 = .4
76.8 – 75.8 = + 1
=6
6 / 6 = 1 (average age expectancy increase each
5 years)
If the current trend continues, the average life
expectancy in 2010 should have be 78.8, in
2015 it should be 79.8 and in 2020 it should be
80.8 years. These are all approximate values
and do not take into account any diseases,
wars, medical/ technological advances or other
events that can have a statistical impact on
these numbers.
Instructional Strategies:
Building on the study of statistics using univariable data in Grades 6 and 7, students are
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Students extend their descriptions and
understanding of variation to the graphical
displays of bivariate data. Scatter plots are
the most common form of displaying
bivariate data in Grade 8.
Students provided with scatter plots and
practice informally finding the line of best
fit.
Students create and interpret scatter plots,
focusing on outliers, positive or negative
association, linearity or curvature. By
changing the data slightly, students can
have a rich discussion about the effects of
the change on the graph.
Students use a graphing calculator or other
technology to determine a linear regression
and discuss how this relates to the graph.
Students informally draw a line of best fit
for a scatter plot and informally measure
the strength of fit.
Discussions include “What does it mean to
be above the line, below the line?” The
study of the line of best fit ties directly to
the algebraic study of slope and intercept.
Students interpret the slope and intercept of
the line of best fit in the context of the data.
Then students can make predictions based
on the line of best fit.
Common Misconceptions:
Students may believe bivariate data is only
displayed in scatter plots. Grade 8.SP.4 in this
cluster provides the opportunity to display
bivariate, categorical data in a table. In general,
students think there is only one correct answer
in mathematics. Students may mistakenly think
their lines of best fit for the same set of data
will be exactly the same as their neighbors.
Because students are informally drawing lines
!
!
Pomona Unified Math News
th
Domain: 8 Grade Statistics and Probability (SP)
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.
of best fit, the lines will vary slightly. To obtain
the exact line of best fit, students would use
technology to find the line of regression, even
then, it depends on the model of line of best fit
used by the technology.
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