Teacher: Aleksandar Mahdjik
Year: 2007-2008
Course: Applied Mathematics
A Introduction to statistics
U
G Essential Questions Content Skills
U Why do people say that there are Terminology: Classify statistical experiments
S three types of lies: lies, damn - statistics as descriptive or inferential
T lies, and statistics? - variable
- descriptive and inferential Differentiate between population
statistics and sample
- population and sample
Why do people say that there are Variables and types of data: Classify variables as
three types of lies: lies, damn - qualitative and quantitative qualitative or quantitative
lies, and statistics? - discerete and continuous
- nominal, ordinal, interval, and Classify variables as discrete or
ratio levels of measurement continuous
Classify levels of measurement
as nominal, ordinal, interval, or
ratio
Why do people say that there are Data collection and sampling Identify different types of data
three types of lies: lies, damn techniques: collection
lies, and statistics? - telephone, mail, and personal
surveys Identify different types of
- random, systematic, stratified, sampling techniques
and cluster sampling
Why do people say that there are Observational and experimental Classify studies as observational
three types of lies: lies, damn studies: - observational study - or experimental
lies, and statistics? experimental study, independent
and dependent variables,
confounding variable
Why do people say that there are Misuses of statistics Recognize misuses of statistics
three types of lies: lies, damn
lies, and statistics?
S Frequency distributions and graphs
E
P Essential Questions Content Skills
T
What type of graph is the best? Organizing data: Create a frequency distribution,
E - categorical, grouped, and manually, and by using Excel
M ungrouped frequency
B distributions
E
R
What type of graph is the best? Graphs: Graph data, manually, and by
- histogram, frequency polygon, using Excel
and ogive
- relative frequency graphs
- distribution shapes
- pareto chart, time series graph,
pie graph, and stem and leaf plot
Data description
Essential Questions Content Skills
What's the difference between Measures of central tendency: Find the measures of central
measures of central tendency, - mean, median, mode, tendency, manually, and by
measures of variation, and midrange, and weighted mean using Excel
measures of position? - measures of central tendency
and distribution shapes
What's the difference between Measures of variation: Find the measures of variation,
measures of central tendency, - range, population and sample manually, and by using Excel
measures of variation, and variance and standard
measures of position? distribution, and coefficient of
variation
What's the difference between Measures of position: Find percentiles and quartiles,
measures of central tendency, - z score manually, and by using Excel
measures of variation, and - percentiles
measures of position? - quartiles Find z scores and outliers
- outliers manually
- boxplots
Graph box plots
O Correlation and regression
C
T Essential Questions Content Skills
O
B What does the coefficient of Scatter plots draw a scatter plot, manually,
E determination tell us? and by using Excel
R
What does the coefficient of Correlation find the coefficient of correlation,
determination tell us? - Pearson product moment manually, and by using Excel
correlation coefficient
- positive and negative linear determine wheter a relationship
relationships is postive or negative, and weak,
- weak, moderate, and strong moderate or strong
linear relationships
What does the coefficient of Regression estimate a line of best fit by
determination tell us? - line of best fit graphing
- equation of a least squares
regression line find the equation of the least
- interpolation and extrapolation regression line, manually, and by
using Excel
differentiate
between interpolation and
extrapolation
predict values (by interpolation or
extrapolation) by using the least
squares regression line
What does the coefficient of Coefficient of determination interpret the coefficient of
determination tell us? - coefficients of determination determination (nondetermination)
and nondetermination
N Probability
O
V Essential Questions Content Skills
E Can probability help us predict Counting rules - fundamental appply fundamental counting
M the future? counting principle, permutations, prinicple, permutations, and
B combinations combinations to solve problems
of the 'how many ways' type
E
R
Can probability help us predict Terminology: use correct terminology
the future? - probability experiment
- outcome differentiate between an outcome
- sample space and an event
- event
- tree diagram
Can probability help us predict Classical probability find classical probability for an
the future? - formula for classical probability event
- equally likely events
- complement of an event find the probability for the
complement of an event
Can probability help us predict Empirical probability find empirical probability for an
the future? - formula for empirical probability event
- law of large numbers
Can probability help us predict Subjective probability recognize when the subjective
the future? probability is used
Can probability help us predict Addition rule for probability determine whether two or more
the future? - mutually exclusive events events are mutually exclusive or
- formula for event 'A or B' for not
mutually exclusive events
- formula for event 'A or B' for find the probability for event 'A or
mutually non-exclusive events B'
Can probability help us predict Multiplication rule for probability determine whether two or more
the future? - independent and dependent events are independent or not
events
- formula for event 'A and B' for understand and find conditional
independent events probability
- conditional probability
- formula for conditional find the probability for event 'A
probability and B'
- formula for event 'A and B' for
dependent events
D Chi-square test for independence
E
C Essential Questions Content Skills
E How do you relate the level of Chi-square test for independence perform a chi-square test for
M significance to your conclusion - null and alternative hypothesis independence, and come up with
B when performing a chi-square - contingency tables a conclusion
test for independence? - expected and observed values
E - chi-square test value
R - degrees of freedom
- level of significance
- critical value
- decision making
J Systems of linear equations and inequalities
A
N Essential Questions Content Skills
U How do systems of linear 2x2 systems of linear equations: solve a 2x2 system of linear
A equations and inequalities apply - graphing method equations using graphing,
R to real world? - substitution method substitution, and elimination
- elimination method methods
Y - inconsistent and dependent
systems determine whether a system is
inconsistent or dependent
How do systems of linear 3x3 systems of linear equations: solve a 3x3 sytem of linear
equations and inequalities apply - substitution method equations by using the
to real world? - elimination method substitution or elimination
method
F Systems of linear equations and inequalities
E
B Essential Questions Content Skills
R How do systems of linear Linear programming: graph linear inequalities and
U equations and inequalities apply - graphing linear inequalities systems of linear inequalities
A to real world? - graphing systems of linear
inequalities find the coordinates of the
R - feasible region vertices of a feasible region
Y - vertices
- bounded and unbounded determine whether a system of
regions linear inequalities is bounded or
- linear programming problems unbounded
solve a linear programming
problem
M Matrices
A
R Essential Questions Content Skills
C What can matrices be used for? Matrix terminology: row, column, determine the dimensions of a
H element, dimensions matrix
What can matrices be used for? Basic matrix operations: perform matrix operations on a
- addition
- subtraction calculator
- multiplication by a scalar
- transposition
Matrix multiplication
What can matrices be used for? Inverses of matrices: determine whether a matrix is
- identity matrices singular or not, and find the
- matrix inverse determinant and inverse on a
- determinant calculator
- singular matrices
What can matrices be used for? Matrix multiplication and systems solve systems of linear equations
of linear equations using matrix multiplication
A Review for Ceneval
P
R Essential Questions Content Skills
I How come a quadratic equation Square of binomials expand a square of a binomial
L can have two solutions?
How come a quadratic equation Factoring quadratic trinomials factor quadratic trinomials
can have two solutions?
How come a quadratic equation Quadratic equations: solve a quadratic equation
can have two solutions? - factoring
- quadratic formula
- completing the square
How come a quadratic equation Factorial, permutations and use factorial, permutation, and
can have two solutions? combinations combination notations
How come a quadratic equation Sigma notation use sigma notation and evaluate
can have two solutions? expressions involving sigma
Binomial Theorem notation
find the expanded form of the nth
pover of a binomial
M Loans and Investments
A
Y Essential Questions Content Skills
What are all the things we should Simple interest: find the interest, final amount,
consider before making an - formulae for simple interest principal, rate, or term, in a
ivestment, and what are all the - discounted loan simple interest problem
things we should consider before - effective rate for a discounted
taking a loan? loan find the effective simple interest
- zero coupon bonds rate for a discounted loan
- commission
solve simple interest problems
involving zero coupon bonds or
commission
What are all the things we should Compound interest: find the final amount, principal,
consider before making an - formula for compound interest rate, or term, in a compound
ivestment, and what are all the - logarithms interest problem
things we should consider before - Rule of 72
taking a loan? - effective rate use The Rule of 72 to find the
doubling time for a compound
interest problem
find the effective compound
interest rate
What are all the things we should Annuities: find the final amount, principal, or
consider before making an - geometric series term, in an annuity problem
ivestment, and what are all the - formula for annuities
things we should consider before - sinking funds
taking a loan?
What are all the things we should Amortization: find the present value of an
consider before making an - present value of an annuity annuity
ivestment, and what are all the - formula for amortization
things we should consider before - unpaid balance find the payment, or unpaid
taking a loan? balance, in an amortization
problem