| Arizona Standards Mathematics Standards
(Adopted 8/26/96)
Standard 2: Data Analysis And
Probability
Students use data collection and analysis, statistics, and
probability to make valid inferences, decisions and arguments and to solve a variety of
real-world problems.
Students know and are able to do the following:
READINESS (Kindergarten) -
2M-R1.Compare and sort objects by their physical
attributes
- 2M-R2.Collect, organize and describe simple data
- 2M-R3.Construct concrete displays of data; read and interpret
elementary tables, graphs and charts
FOUNDATIONS (Grades 1-3) -
2M-F1.Collect and analyze data using the concepts of
largest, smallest, most often, least often and middle
PO 1. Collect and record data from surveys (e.g., favorite
color or food, height, ages) or experiments
PO 2. Organize (e.g., sorting, sequencing, tallying)
information from surveys or experiments
PO 3. Identify largest, smallest, most often recorded (i.e.,
mode), least often and middle (i.e., median) using sorted data
PO 4. Formulate questions from organized data
-
2M-F2.Construct, read and interpret displays of data to
make valid decisions, inferences and predictions
PO 1. Make and label a graph (horizontal bar, vertical bar,
picture graph or tally chart) from organized data
PO 2. Answer questions about a circle graph (i.e., pie graph)
divided into halves and fourths
PO 3. Answer questions about a pictograph where each symbol
represents multiple units
PO 4. Write a title representing the main idea of a graph
PO 5. Locate points on a line graph (grid) using ordered
pairs
PO 6. Draw conclusions (e.g., valid decisions, conjectures
and predictions) from graphed data
PO 7. Formulate questions from graphs, charts and tables
PO 8. Solve problems using graphs, charts and tables (e.g.,
given a bar graph or preferred flavors of ice cream, students have to decide what flavors
of ice cream to order)
-
2M-F3.Predict and measure the likelihood of events and
recognize that the results of an experiment may not match predicted outcomes
Note: Probability experiments are simple
one-step activities, e.g., tossing a two-colored counter
PO 1. Collect and record data from a probability experiment
PO 2. Organize (e.g., sorting, sequencing, tallying) data
from a probability experiment
PO 3. Name the possible outcomes of the probability
experiment
PO 4. Predict the most likely or least likely outcome in
probability experiments
PO 5. Compare the outcome of the experiment to the
predictions
-
2M-F4.Understand the concept of sample (i.e., that a
larger sample of observed outcomes leads to more reliable information)
PO 1. Compare data from probability experiments in which the
experiments are performed a different number of times with the given expected outcomes
(e.g., toss a two-colored counter 10 times and record the data; toss the counter 20 times
and record the data; compare the results to the expected outcome [1 out of 2])
ESSENTIALS (Grades 4-8) -
2M-E1.Construct, read, analyze and interpret tables,
charts, graphs and data plots (e.g., box-and-whisker, stem-and-leaf, and scatter plots)
PO 1. Construct
- bar graphs, line graphs, frequency tables and Venn diagrams (Grades
4-5)
- histograms, stem-and-leaf plots, scatter plots, circle graphs,
and flow charts (Grades 6-8)
PO 2. Interpret and analyze data from graphical
representations and draw simple conclusions
- bar graphs, line graphs, circle graphs, frequency tables and
Venn diagrams (Grades 4-5)
- histograms, stem-and-leaf plots, scatter plots, circle graphs
and flow charts (Grades 6-8)
PO 3. Choose an appropriate graphical format to organize and
represent data (Grades 6-8
- 2M-E2.Make valid inferences, predictions and arguments based
on statistical analysis
PO 1. Formulate predictions from a given set of data and
justify predictions (Grades 4-5, 6-8)
PO 2. Compare a given prediction with the results of an
investigation (Grades 4-5, 6-8)
PO 3. Critique the conclusions and recommendations of
others’ statistics (Grades 6-8)
PO 4. Consider the effects of missing or incorrect
information (Grades 6-8)
2M-E3.Display and use measures of range and central
tendency (i.e., mean, median and mode)
PO 1. Find the mean, median, mode and range of data using
concrete and illustrative models (Grades 4-5)
PO 2. Find the mean, median, mode and range of a data set
(Grades 6-8)
PO 3. Choose appropriate measures of central tendencies
to describe given or derived data (Grades 6-8)
- 2M-E4.Use counting strategies to determine all the possible
outcomes of a particular event (e.g., the number of ways students can line up to have
their pictures taken)
PO 1. Find all possible outcome sets involving
- two sets of objects (e.g., shirts and pants) (Grades 4-5)
- two or more sets of objects (Grades 6-8)
PO 2. Find all possible arrangements given a set (e.g.,
"How many ways can you arrange a set of books on a shelf?") (Grades 6-8)
- 2M-E5.Determine probabilities through experiments and/or
simulations and compare the results with the mathematical expectation
PO 1. Make predictions from the results of a
student-generated experiment (empirical probability)
- single events (e.g., spinners) (Grades 4-5)
- two-stage events (e.g., two spinners) (Grades 6-8)
PO 2. Determine and compare experimental (empirical) and
mathematical (theoretical) probabilities (e.g., flipping two-colored counters) (Grades
6-8)
PO 3. Describe events that are certain or impossible (Grades
4-5)
PO 4. Express probability as a fraction, zero or one (Grades
6-8)
PO 5. Identify outcomes that are more likely, less likely
or equally likely to occur (Grades 4-5)
PROFICIENCY (Grades 9-12) -
2M-P1.Construct and draw inferences including measures of
central tendency, from charts, tables, graphs and data plots that summarize data from
real-world situations
PO 1. Organize collections of data into frequency charts,
stem-and-leaf plots, scatter plots and matrices
PO 2. Construct histograms, line graphs, circle graphs and
box-and-whisker plots
PO 3. Draw inferences from collections of data
PO 4. Evaluate the reasonableness of conclusions drawn from
data analysis
PO 5. Use mean, median, mode, quartiles and range as a means
for effective decision making in analyzing the data and the outliers
PO 6. Explain graphic misrepresentations and distortions of
sets of data
- 2M-P2.Use appropriate technology
(e.g., graphing calculators, computer software) to display and
analyze data
PO 1. Use appropriate technology
to display data as lists, tables, matrices and plots
PO 2. Use appropriate
technology to calculate mean, median, mode, minimum and maximum
PO 3. Use appropriate
technology to predict patterns in sets of data (e.g., "Does
a scatter plot appear to be linear?")
- 2M-P3.Apply curve fitting to make predictions from data
PO 1. Draw a line or a curve which closely fits a scatter
plot
PO 2. Make a prediction from a pattern in plots of data
- 2M-P4.Explain the effects of sampling on statistical claims
and recognize misuses of statistics
PO 1. Differentiate between sampling and census
PO 2. Differentiate between a biased and an unbiased sample
PO 3. Recognize the impact of interpreting data from a biased
sample
PO 4. Distinguish the effects of using statistical measures
obtained from a sample vs. those obtained from a census
PO 5. Recognize the misinterpretations of data from different
representations of those same data
PO 6. Determine the validity of sampling methods in studies
- 2M-P5.Design and conduct a statistical experiment to study a
problem and interpret and communicate the outcomes
PO 1. Design a statistical experiment based on a given
hypothesis
PO 2. Create an appropriate data-gathering instrument (e.g.,
biased vs. unbiased questions, multiple choice vs. open-ended)
PO 3. Organize collected data into an appropriate graphical
representation
PO 4. Draw and support inferences that are based on data
analysis
- 2M-P6.Use experimental or theoretical probability, as
appropriate, to represent and solve problems involving uncertainty
PO 1. Recognize whether experimental or theoretical methods
were used to calculate a particular probability
PO 2. Use experimental observations to estimate probabilities
of entire populations
PO 3. Distinguish between independent and dependent events
PO 4. Solve probability problems involving and and or
statements, with and without replacement
- 2M-P7.Use simulations to estimate
probabilities
PO 1. Design
appropriate simulations to estimate probabilities of real-world
situations (e.g., disk toss, cube toss, technological simulations)
PO 2. Use simulations
to estimate probabilities of real-world situations
- 2M-P8.Solve real-world problems by using combinations and
permutations
PO 1. Use a tree diagram and a chart of possible outcomes to
count probable outcomes of an event
PO 2. Determine when to use combinations in counting objects
PO 3. Determine when to use permutations in counting objects
PO 4. Use combinations and permutations to solve real-world
problems not requiring the use of formulas
- 2M-P9.Describe, in general terms, the normal curve and use its
properties to answer questions about sets of data that are assumed to be normally
distributed
PO 1. Determine if data gathered from a real-world situation
fits a normal curve
PO 2. Describe the central tendency characteristics of the
normal curve
PO 3. Make simple predictions from data represented on a
given normal curve
- 2M-P10.Explain the concept of a random variable
PO 1. Distinguish situations where a random variable is
needed or used
PO 2. Use a random number table
or technology to generate random numbers in modeling real-life
situations (e.g., select randomly who belongs in what group)
- 2M-P11.Apply measures of central tendency, variability and
correlation
PO 1. Apply the concepts of mean, median, mode and range to
draw conclusions about data
PO 2. Draw conclusions about the "spread" of data
given the variance and standard deviation (e.g., compare sets of data with the same
central tendency, but with different variance)
PO 3. Determine, from a given plot of data, whether it has
strong or weak, positive or negative correlation
DISTINCTION (Honors)
- 2M-D1.Transform data to aid in data interpretation and
prediction
- 2M-D2.Test hypotheses using appropriate statistics
- 2M-D3.Explain the concept of a random variable to generate and
interpret probability distributions including binomial, uniform and normal
- 2M-D4.Apply the concept of a random variable to generate and
interpret probability distributions including binomial, uniform and normal
- 2M-D5.Apply curve fitting to determine the strength of the
relationship between two data sets and to make predictions from data
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