Teacher: CORE Introductory Statistics and Probability
Course: Introductory Statistics and Probability
Year: 2014-15
Month: All Months
Nature of Probability and Statistics
Standards
Essential Questions
Assessments
S-IC.3-Recognize the purposes of and
differences among sample surveys,
experiments, and observational studies;
explain how randomization relates to each.
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.6-Evaluate reports based on data.
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.
1. What type of variables,
Quiz on terminology
quantitative or qualitative, are
the following terms: height,
marital status, and car colors?
2. Which sampling technique
is being used when we: choose
every 4th person, and draw
numbers from a hat?
Skills
Content
Lessons
1. Use of descriptive and
inferential statistics
2. Using variables and learning
about different types of data
3. Collecting data and use of
sampling techniques
4. Learning the history of
probability and statistics
1. Definitions and terminology Is it qualitative or
quantitative?
2. Qualitative
and quantitative variables
Resources
Elementary Statistics, A
Step by Step Approach,
second edition- Allan G.
Bluman, Wm. C. Brown
Publishers
3. Levels of measurement
4. Random sampling
5. Systematic sampling
3. Which type of statistics is
used for the following,
inferential or
descriptive: Average grade is
89%; Chance of you being
robbed next year is 15%.
6. Stratified sampling
7. Cluster sampling
Frequency Distributions and Graphs
Standards
Essential Questions
S-IC.1-Understand statistics as a process for
making inferences about population
parameters based on a random sample from
that population.
S-IC.6-Evaluate reports based on data.
S-ID.1-Represent data with plots on the real
number line (dot plots, histograms, and box
plots).
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.
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).
1. What is the difference
between grouped and
ungrouped frequency
distributions?
Assessments
Skills
Content
1. Organizing data
1. Tallies
2. Graphing data
2. Grouped frequency
distributions
3. Interpreting data
2. How can I tell if the graph is
a histogram or a bar graph?
3. Ungrouped frequency
distributions
3. In a pie graph, how do I
determine the angle measure
for each section?
4. Histograms
5. Frequency Polygons
6. Ogives
7. Bar graphs and pie graphs
8. Pictographs, stem and leaf
plots, and other graphs
Lessons
Resources
Elementary Statistics, A
Step by Step Approach,
second edition- Allan G.
Bluman, Wm. C. Brown
Publishers
Data Description
Essential
Questions
Standards
S-ID.1-Represent data with plots on the real number line
(dot plots, histograms, and box plots).
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.
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.
Assessments
Skills
1. What is
Mean, median, and mode
1. Calculating by hand
another name for quiz of grouped and
different measures of central
the mean?
ungrouped data
tendency.
2. What do we
2. Calculating by calculator
call the number Standard deviation and
the measures of central
or numbers that variance quiz for grouped and tendency.
appear more
ungrouped data
3. Understanding and
than any other?
applying Chebyshev's
3. What is meant Quiz on Chebyshev's Thm,
theorem.
by the variance? empirical rule and box and
4. Applying box and whisker
4. What is meant whisker plots
plots.
by an outlier?
Test on this unit
Content
Lessons
1. means for grouped and
M&M Lab 2
ungrouped data
2. mode for grouped and
ungrouped data
3. different distribution shapes
4. midrange
5. range
6. variance and standard deviation
7. coefficient of variation
8. Chebyshev's theorem
9. empirical or normal rule
10. Deciles, quartiles, and box and
whisker plots
Resources
Elementary Statistics, A
Step By Step ApproachSecond Edition
Counting Rules
Standards
Essential Questions Assessments
S-CP.1-(+) Define a random variable for a quantity of
1. How many license
Multiplication rule 1 and
interest by assigning a numerical value to each event in plate numbers can be
2 quiz
a sample space; graph the corresponding probability
created if there are 3
distribution using the same graphical displays as for data numbers?
distributions.
2. How do we handle no
S-CP.6-(+) Use probabilities to make fair decisions (e.g., repeats?
drawing by lots, using a random number generator).
3. What does ! mean in a
S-CP.8-(+) Apply the general Multiplication Rule in a
math class?
uniform probability model, P(A and B) = P(A)P(B|A) =
4. How do we find 4!?
P(B)P(A|B), and interpret the answer in terms of the
5. In which of these is
model.
order important,
S-CP.9-(+) Use permutations and combinations to
permutation or
compute probabilities of compound events and solve
combinations?
problems.
Skills
Content
Lessons
Resources
1. calculating total outcomes
2. learning and applying
permutations
3. learning and applying
combinations
4. learning and applying tree
diagrams
1.
2.
3.
4.
Probability
Lab
Elementary Statistics, A
Step By Step ApproachSecond Editon
Skills
Content
Lessons Resources
1. concepts of classical, empirical
and subjective probability
2. addition rules 1 and 2
3. multiplication rules 1 and 2
4. dependend and independent
events
5. conditional probability
6. Baye's Theorem
7. Rule for complementary events
Probability Elementary Statistics, A
Lab 2
Step By Step ApproachSecond Edition
multiplication rule 1 and 2
permutation rules 1,2 and 3
combination rule
tree diagrams
Probability
Standards
Essential Questions Assessments
S-CP.1-(+) Define a random variable for a quantity of interest 1. Find the 3P2
by assigning a numerical value to each event in a sample
space; graph the corresponding probability distribution
2. What is the difference
using the same graphical displays as for data distributions. between dependent
S-CP.5-(+) Weigh the possible outcomes of a decision by
events and independent
assigning probabilities to payoff values and finding expected event?
values.
S-CP.8-(+) Apply the general Multiplication Rule in a uniform 3. What is the probability
probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and of getting at least one
interpret the answer in terms of the model.
head when rolling 3 dice?
Probability quiz 1addition rules
1. writing sample spaces
2. using the addition rules for
probability
Probability quiz 2- 3. calculating using the
multiplication rules multiplication rules for
probability
Unit test
4. setting up and solving using
Bayes Theorem
5. calculating probabilities
using complementary events
Probability Distributions
Standards
Essential Questions
Assessments
S-CP.2-(+) Calculate the expected value of a
random variable; interpret it as the mean of
the probability distribution.
S-CP.3-(+) Develop a probability distribution
for a random variable defined for a sample
space in which theoretical probabilities can be
calculated; find the expected value.
S-CP.4-(+) Develop a probability distribution
for a random variable defined for a sample
space in which probabilities are assigned
empirically; find the expected value.
S-CP.5-(+) Weigh the possible outcomes of a
decision by assigning probabilities to payoff
values and finding expected values.
S-CP.5a-Find the expected payoff for a game
of chance.
S-CP.5b-Evaluate and compare strategies on
the basis of expected values.
1. In a probability distribution Quiz on the
the sum of all the probabilities probability
equals what number?
distributions
2. In these distributions, what Quiz on binomial
must be true about each of the distributions
entries?
Test on this unit
3. What makes a game of
chance fair?
4. What formula do we use to
find the mean of a binomial
distribution?
Skills
Content
1. write probability distributions
1. probability distributions Probability Lab 3
2. use measures of central
tendency
2. mean for probability
distributions
3. calculate the expectation of an 3. variance and standard
event
deviation for probability
distributions
4. calculate the measures of
central tendency for a binomial
4. expectations
distribution
5. binomial experiments
6. mean of binomial
experiments
7. variance and standard
deviation for a binomial
distribution
Lessons
Resources
Elementary Statistics, A
Step By Step ApproachSecond Edition