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[MATHEMATICS: STATISTICS] December 14, 2007
Statistics
1
[MATHEMATICS: STATISTICS] December 14, 2007
Statistics Summary
Strand
Data Analysis, Statistics,
and Probability
Data Analysis, Statistics,
and Probability
Data Analysis, Statistics,
and Probability
Total
Standard
Topic
11
Data Collection and Display
Number of
Elements
6
12
Data Interpretation
4
13
Predictions and Inferences
2
12
2
[MATHEMATICS: STATISTICS] December 14, 2007
Topic: Data Collection and Display (1)
Strand: Data Analysis, Statistics, and Probability
Standard 11: FLUENCY WITH DATA: Pose questions and collect, organize, and
represent data to answer those questions.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught, such as:
 Implement an experiment and list all your variables, controls, hypothesis, etc.
Level 3.5
Level 3.0
While involved in tasks regarding data collection and display the student will:
 Develop a hypothesis for an investigation or experiment (e.g., develop and
defend a hypothesis for an investigation). MA.S.11.1
 Recognize the variables and controls in an experiment or expectation (e.g.,
identify the variable in an investigation or experiment, sets a control, and
explains the need for a control). MA.S.11.2
 Select appropriate display for a data set (frequency table, histogram, line
graph, bar graph, stem-and-leaf plot, box-and-whisker plot, scatter plot) (e.g.,
choose an appropriate display for a data set and explain why it is an
appropriate choice). MA.S.11.3
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o Hypothesis, variables, control, data
 recognizing and recalling the accuracy of basic solutions and information such
as:
o Identify the hypothesis for an experiment.
o Recognize that experiments have variables and controls.
o Recognize similarities and differences between displays for data
sets.
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
3
[MATHEMATICS: STATISTICS] December 14, 2007
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0

Level 3.0

Level 2.0
4
[MATHEMATICS: STATISTICS] December 14, 2007
Topic: Data Collection and Display (2)
Strand: Data Analysis, Statistics, and Probability
Standard 11: FLUENCY WITH DATA: Pose questions and collect, organize, and
represent data to answer those questions.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught, such as:
 Using an experiment, make two graphs of the same piece of information, one
misleading one fair, and have the student talk about how the same graphs can
be used to mislead the general public.
Level 3.5
Level 3.0
While involved in tasks regarding data collection and display the student will:
 Recognize features of representations of data that can produce misleading
interpretations (e.g., explain how a data display was made to produce
misleading interpretations). MA.S.11.4
 Recognize sampling, randomness, bias, and sampling size in data collection
and interpretation (e.g., consider possible bias and sampling errors when
interpreting data and propose options to correct the errors). MA.S.11.5
 Describe the purpose and function of a variety of data collection methods
(census, sample surveys, experiment, observation) (e.g., explain the
differences between data collection methods). MA.S.11.6
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o random, bias, skewed data
 recognizing and recalling the accuracy of basic solutions and information such
as:
o Recognizes that data can be skewed.
o Recognizes the terms sampling, randomness, and bias.
o Recognize a variety of data collection methods.
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
5
[MATHEMATICS: STATISTICS] December 14, 2007
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0

Level 3.0

Level 2.0
6
[MATHEMATICS: STATISTICS] December 14, 2007
Topic: Data Interpretation
Strand: Data Analysis, Statistics, and Probability
Standard 12: STATISTICS: Interpret data using methods of exploratory data
analysis.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught, such as:
 Using baseball statistics try to predict how a certain player will perform by
using best fit curves (opportunity to talk about sabermetrics).
Level 3.5
Level 3.0
While engaged in tasks involving data interpretation the student will:
 Use measures of central tendency and spread to interpret data (e.g., interpret a
data set based on the mean and standard deviation). MA.S.12.1
 Interpret data based on the correlation coefficient of two variables (e.g.,
identify a data set that has a positive correlation and makes an interpretation
based on that trend). MA.S.12.2
 Describe the effect of sample size and transformation on the shape, center, and
spread of data (e.g., explain the effect on shape, center, and spread of data, if
the unit of measure is changed). MA.S.12.3
 Use the line or curve of best fit to interpret data (e.g., draw the line (or curve)
of best fit on a graph and uses it to describe any trends that exist). MA.S.12.4
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o Sample size, central tendaency
 recognizing and recalling the accuracy of basic solutions and information such
as:
o Recognize measure of central tendency.
o Recognize the correlation coefficient of two variables.
o Recognizes that sample size and transformation can affect shape,
center, and spread of data.
o Recognize the line or curve of best fit.
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
7
[MATHEMATICS: STATISTICS] December 14, 2007
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0

Level 3.0

Level 2.0
8
[MATHEMATICS: STATISTICS] December 14, 2007
Topic: Predictions and Inferences
Strand: Data Analysis, Statistics, and Probability
Standard 13: DATA ANALYSIS: Develop and evaluate inferences, predictions, and
arguments that are based on data.
Statistics
Level 4.0
In addition to Level 3.0, in-depth inferences and applications that go beyond
what was taught, such as:
 Given a random set of data, interpret the results and explain the results
statistically to the class.
Level 3.5
Level 3.0
While engaged in tasks involving predictions and inferences the student will:
 Recognize that some data can be represented algebraically (linear, quadratic,
exponential, sinusoidal) (e.g., identify data that is linear (sales tax), quadratic,
(height of a bouncing ball), exponential (growth of certificate of deposit), or
sinusoidal (number of daylight hours throughout the year). MA.S.13.1
 Use interpolation and extrapolation to make predictions and inferences about
data (e.g., analyze the trend in a data set and make interpolations and
extrapolations based on the trend). MA.S.13.2
The student exhibits no major errors or omissions.
Level 2.5
Level 2.0
In addition to Level 3.0 performance, in-depth inferences and applications with
partial success.
No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
There are no major errors or omissions regarding the simpler details and
processes as the student:
 recognizes or recalls specific terminology such as:
o (See Below)
 recognizing and recalling the accuracy of basic solutions and information such
as:
o Recognizes the terms: linear, quadratic, exponential, sinusoidal.
o Recognizes the terms interpolation and extrapolation.
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes.
Level 1.5
Level 1.0
Level 0.0
Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
With help, a partial understanding of some of the simpler details and processes and some of the
more complex ideas and processes.
Level 0.5
With help, a partial understanding of some of the simpler details and processes but
not the more complex ideas and processes.
Even with help, no understanding or skill demonstrated.
9
[MATHEMATICS: STATISTICS] December 14, 2007
Sample Tasks for Levels 4.0, 3.0, & 2.0
Level 4.0

Level 3.0

Level 2.0
10