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Transcript
1. Use one of the four basic sampling methods to distribute surveys appropriately. (Random,
systematic, stratified, and cluster)
a. MA.912.S.2.2:
Apply the definition of random sample and basic types of sampling, including
representative samples, stratified samples, censuses.
b. CCSS.Math.Content.HSS-IC.A.1 Understand statistics as a process for making
inferences about population parameters based on a random sample from that
population
2. Recognize and prevent faulty questions on a survey and other factors that can bias
responses.
a. MA.912.S.2.3:
Identify sources of bias, including sampling and non-sampling errors
3. Develop a survey that accurately measures the data necessary to answer the driving
questions.
a. MA.912.S.1.1:
Formulate an appropriate research question to be answered by collecting data or
performing an experiment.
b. MA.912.S.1.2:
Determine appropriate and consistent standards of measurement for the data to be
collected in a survey or experiment.
c. MA.912.S.2.1:
Compare the difference between surveys, experiments, and observational studies
and what types of questions can and cannot be answered by a particular design.
d. CCSS.Math.Content.HSS-IC.B.3 Recognize the purposes of and differences
among sample surveys, experiments, and observational studies; explain how
randomization relates to each
4. Determine sample spaces and find the probability of an event, using classical probability
or empirical probability. (students can find the classical probability before issuing the
surveys and empirical probability once they have the results from the surveys)
a. MA.912.P.2.2:
Determine probabilities of independent events.
b. MA.912.P.1.1:
Use counting principles, including the addition and the multiplication principles,
to determine size of finite sample spaces and probabilities of events in those
spaces.
c. MA.912.P.2.1:
Determine probabilities of complementary events, and calculate odds for and
against the occurrence of events.
d. CCSS.Math.Content.HSS-CP.A.1 Describe events as subsets of a sample space
(the set of outcomes) using characteristics (or categories) of the outcomes, or as
unions, intersections, or complements of other events (“or,” “and,” “not”).
e. CCSS.Math.Content.HSS-CP.B.7 Apply the Addition Rule, P(A or B) = P(A) +
P(B) – P(A and B), and interpret the answer in terms of the model.
f. CCSS.Math.Content.HSS-CP.B.8 (+) Apply the general Multiplication Rule in a
uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and
interpret the answer in terms of the model.
5. Find the probability of compound events, using the addition or multiplication
rules. (Have the students look at the probability of when the consumer likes one thing or
another; observe the case when things are mutually exclusive or not)
a. MA.912.P.1.2:
Use formulas for permutations and combinations to count outcomes and
determine probabilities of events.
b. CCSS.Math.Content.HSS-CP.A.2 Understand that two events A and B are
independent if the probability of A and B occurring together is the product of
their probabilities, and use this characterization to determine if they are
independent.
c. CCSS.Math.Content.HSS-CP.B.9 (+) Use permutations and combinations to
compute probabilities of compound events and solve problems.
6. Find the conditional probability of an event. (this is the probability of an event given the
outcome of another one; make sure that students ask if/then type questions; look at the
candy example)
a. CCSS.Math.Content.HSS-CP.A.2 Understand that two events A and B are
independent if the probability of A and B occurring together is the product of
their probabilities, and use this characterization to determine if they are
independent.
b. CCSS.Math.Content.HSS-CP.A.3 Understand the conditional probability
of A given B as P(A andB)/P(B), and interpret independence of A and B as saying
that the conditional probability of A givenB is the same as the probability of A,
and the conditional probability of B given A is the same as the probability of B.
c. CCSS.Math.Content.HSS-CP.A.5 Recognize and explain the concepts of
conditional probability and independence in everyday language and everyday
situations
d. CCSS.Math.Content.HSS-CP.B.6 Find the conditional probability
of A given B as the fraction of B’s outcomes that also belong to A, and interpret
the answer in terms of the model.
7. Construct a probability distribution for a random variable. (A table of the probability of
each event in the sample space before distribution)
a. CCSS.Math.Content.HSS-MD.A.1 (+) Define a random variable for a quantity of
interest by assigning a numerical value to each event in a sample space; graph
the corresponding probability distribution using the same graphical displays as
for data distributions.
b. CCSS.Math.Content.HSS-MD.A.2 (+) Calculate the expected value of a random
variable; interpret it as the mean of the probability distribution.
c. CCSS.Math.Content.HSS-MD.A.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.
d. CCSS.Math.Content.HSS-MD.A.4 (+) Develop a probability distribution for a
random variable defined for a sample space in which probabilities are assigned
empirically; find the expected value
8. Find the mean, variance, and standard deviation for the variable of a binomial
distribution. (it looks a bit plug and chug, but may need this as above)
a. MA.912.S.3.4:
Calculate and interpret measures of variance and standard deviation. Use these
measures to make comparisons among sets of data
b. CCSS.Math.Content.HSS-IC.B.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.
9. Organize (survey) data using a frequency distribution
10. Represent data in frequency distributions graphically using histograms, frequency
polygons and ogives (none of these are appropriate for discrete categorical data
collection; use for pricing preferences?) and using bar graphs, Pareto Charts, time series
graphs, and pie graphs (good for discrete categorical stuff)
a. CCSS.Math.Content.HSS-ID.A.1 Represent data with plots on the real number
line (dot plots, histograms, and box plots).
b. MA.912.S.3.2:
Collect, organize, and analyze data sets, determine the best format for the data and
present visual summaries from the following:
i.
bar graphs
ii. line graphs
iii. stem and leaf plots
iv.
circle graphs
v.
histograms
vi.
box and whisker plots
vii.
scatter plots
viii. cumulative frequency (ogive) graphs
11. Draw and interpret a stem and leaf plot ( not good for discrete, but could work with
continuous numbers)
a. CCSS.Math.Content.HSS-ID.A.1 Represent data with plots on the real number
line (dot plots, histograms, and box plots).
b. MA.912.S.3.1:
Read and interpret data presented in various formats. Determine whether data is
presented in appropriate format, and identify possible corrections. Formats to
include:
i.
bar graphs
ii. line graphs
iii. stem and leaf plots
iv.
circle graphs
v.
histograms
vi.
box and whiskers plots
vii.
scatter plots
viii. cumulative frequency (ogive) graphs
c. MA.912.S.3.2:
Collect, organize, and analyze data sets, determine the best format for the data and
present visual summaries from the following:
ix. bar graphs
x. line graphs
xi. stem and leaf plots
xii. circle graphs
xiii. histograms
xiv. box and whisker plots
xv. scatter plots
xvi. cumulative frequency (ogive) graphs
12. Summarize data, using measures of central tendency, such as the mean, median, mode,
and midrange. (Benchmark lesson or investigation?)
a. MA.912.S.3.3:
Calculate and interpret measures of the center of a set of data, including mean,
median, and weighted mean, and use these measures to make comparisons
among sets of data.
13. Find the mean, variance, standard deviation, and expected value for a discrete random
variable. (Students can do this for each answer after distribution)
a. MA.912.S.3.4:
Calculate and interpret measures of variance and standard deviation. Use these
measures to make comparisons among sets of data
14. Describe data, using measures of variation, such as the range, variance, and standard
deviation. (Same as above)
a. MA.912.S.3.4:
Calculate and interpret measures of variance and standard deviation. Use these
measures to make comparisons among sets of data
15. Justify whether or not the survey was an appropriate measure of data to answer the
driving question.
a. CCSS.Math.Content.HSS-IC.A.2 Decide if a specified model is consistent with
results from a given data-generating process, e.g., using simulation.
b. CCSS.Math.Content.HSS-IC.B.6 Evaluate reports based on data
c. CCSS.Math.Content.HSS-MD.B.7 (+) Analyze decisions and strategies using
probability concepts (e.g., product testing, medical testing, pulling a hockey
goalie at the end of a game)
CCSS.Math.Content.HSS-CP.A.4 Construct and interpret two-way frequency tables of data
when two categories are associated with each object being classified. Use the two-way table as a
sample space to decide if events are independent and to approximate conditional
probabilities. For example, collect data from a random sample of students in your school on
their favorite subject among math, science, and English. Estimate the probability that a
randomly selected student from your school will favor science given that the student is in tenth
grade. Do the same for other subjects and compare the results.
Common Core Math Glossary Terms:
(Alphabetical Order)
Independently combined probability models. Two probability models are said to be combined
independently if the probability of each ordered pair in the combined model equals the product
of the original probabilities of the two individual outcomes in the ordered pair.
Mean. A measure of center in a set of numerical data, computed by adding the values in a list
and then dividing by the number of values in the list.4 Example: For the data set {1, 3, 6, 7, 10,
12, 14, 15, 22, 120}, the mean is 21.
Mean absolute deviation. A measure of variation in a set of numerical data, computed by
adding the distances between each data value and the mean, then dividing by the number of data
values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute
deviation is 20.
Median. A measure of center in a set of numerical data. The median of a list of values is the
value appearing at the center of a sorted version of the list—or the mean of the two central
values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12,
14, 15, 22, 90}, the median is 11.
Probability distribution. The set of possible values of a random variable with a probability
assigned to each.
Probability. A number between 0 and 1 used to quantify likelihood for processes that have
uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people,
tossing a ball at a target, or testing for a medical condition).
Probability model. A probability model is used to assign probabilities to outcomes of a chance
process by examining the nature of the process. The set of all outcomes is called the sample
space, and their probabilities sum to 1. See also: uniform probability model.
Random variable. An assignment of a numerical value to each outcome in a sample space.
Rational expression. A quotient of two polynomials with a non-zero denominator.
Sample space. In a probability model for a random process, a list of the individual outcomes that
are to be considered.
Uniform probability model. A probability model which assigns equal probability to all
outcomes. See also: probability model.