# Applied Probability and Statistics

A variety of topics in business, information technology, and education require mathematical calculations and the ability to analyze statistical information.

Throughout this course, the symbol on the right will provide insight between the material being covered in a particular lesson and how that particular math or analysis skill is performed in the field.

## Module 1: Basic Numeracy & Calculation Skills

• Identify whole numbers, integers, or rational numbers from a finite set of real numbers
• Order a finite set of real numbers with or without a number line
• Apply the mathematical operations to whole numbers
• Apply the mathematical operations to integers
• Apply the mathematical operations to numbers with exponents
• Apply the order of operations correctly to a given numerical expression
• Approximate a solution to a mathematical problem using estimation skills
• Identify the prime factorization of a given whole number
• Identify the greatest common factor of two given whole numbers
• Calculate the square root of a whole number

## Module 2: Fractions, Decimals, & Percentages

• Identify equivalent fractions
• Identify the Least Common Denominator of two fractions
• Apply the mathematical operations of addition, subtraction, multiplication, and division to fractions
• Identify place values for a given decimal number
• Apply a given rounding algorithm for decimal numbers
• Apply the mathematical operations of addition, subtraction, multiplication, and division to decimals
• Apply the mathematical operations of addition, subtraction, multiplication, and division to percentage values
• Solve for an unknown quantity using ratios in the context of a proportion
• Convert between decimals, fractions, and percentages
• Apply basic unit conversions for household and metric measures

## Module 3: Basic Algebra

• Identify the inverse operation that corresponds to a given operation
• Evaluate a given algebraic expression using the distributive property
• Combine like terms to simplify a given algebraic expression
• Evaluate a given algebraic expression using substitution
• Identify an algebraic expression or equation that defines a given pattern of relationships for a given real world problem
• Solve a given linear equation of a specified form
• Predict solution to a real world problem given an algebraic equation
• Solve a given linear equation with fraction coefficients and constants of the form
(ab)x=cdabx=cd
• Solve a given linear inequality
• Identify a graphical representation of the solution
• Identify the graph of given coordinates on a coordinate plane
• Identify the slope when given a graph of a linear equation
• Identify the correct graph for a given linear equation of the form y=mx+b

## Module 4: Descriptive Statistics for a Single Variable

• Apply the standard deviation rule to a special case of normal distributions
• Identify the appropriate numerical measures for a given set of data in different contexts
• Relate measures of center and spread to the shape of the distribution
• Calculate the mean, median, mode, quartiles, range, and interquartile range for a set of quantitative data
• Evaluate data from several different graphical displays of a distribution of a categorical variable (bar chart, pie chart) and of a quantitative variable (histogram, stem plot, box plot)
• Describe the distribution of a categorical variable in context
• Describe the distribution of a quantitative variable in context: a) describe the overall pattern, b) describe striking deviations from the pattern
• Identify the appropriate graphical display for a given set of data in different contexts
• Explain how graphical displays can be used to misrepresent data

## Module 5: Descriptive Statistics for Two Variables

• Classify a data analysis situation according to the role-type classification
• Identify the appropriate graphical display for a given classification in different contexts
• Identify the appropriate numerical measures for a given classification in different contexts
• Compare conditional percentages in a two-way table
• Summarize distributions of two variables
• Determine the relationship between two quantitative variables, when given a graph
• Describe the overall pattern and the striking deviations in a graph of two variables

## Module 6: Correlation & Regression

• Identify sampling methods, common errors related to sampling, and observational and experimental study designs
• Explain the distinction between association and causation
• Identify potential lurking variables
• Explain the phenomenon of Simpson’s Paradox as it relates to interpreting the relationship between two variables
• Estimate the value of the correlation coefficient between two variables from a scatterplot
• Interpret the value of the correlation coefficient between two variables
• Recognize the limitations of the correlation coefficient as a numerical measure of the association between two quantitative variables
• Identify regression analysis applications for purposes of description and prediction
• Interpret the simple least squares linear regression equation for a set of data in regards to the overall pattern
• Interpret the simple least squares linear regression equation to make a prediction
• Determine whether a regression model is significant
• Identify potential problems if regression analysis is used incorrectly

## Module 7: Probability

• Relate the probability of an event to the likelihood of the event occurring
• Explain how relative frequency can be used to estimate the probability of an outcome or an event
• Determine the sample space of a given random experiment
• Find the probability of events in the case in which all outcomes are equally likely
• Determine if two events are disjoint
• Apply the addition rule to find the probability of a given set of disjoint events
• Determine if two events are independent
• Apply the multiplication rule to find the probability of a given set of independent events
• Apply basic probability concepts to interpret and solve mathematical problems
• Find probabilities using Venn diagrams or probability tables as aids
• Explain the concept of conditional probability and properly use the probability notation for a conditional event
• Identify an example that represents a case of conditional probability
• Determine the probability of an event using principles of conditional probability