Statistics

Statistics

1. Data: Information from observations, measurements or responses

   • Statistics: The science of collecting, interpreting, and organizing data
     • Population: Collection of all outcomes and measurements
       • Parameter: A numerical description of a population characteristic
     • Sample: A part of a population
       • Statistic: A numerical description of a sample characteristic

2. Chapter 1: Introduction to Statistics

   • Qualitative Data: Consists of non-numerical entries and attributes
     • Nominal level of measurement: Are qualitative only, and all data is categorized using names, labels or qualities.
       • Ratio levels of measurement: Are similar to data at the interval level with the added property that a zero entry is an adherent zero
   • Quantitative data: Consists of numerical measurements and counts
     • Ordinal level of measurement: Are qualitative and quantitative, and are arranged in order
       • Interval level of measurement: can be ordered, and meaningful differences between data entries can be calculated
   • Perform an experiment
     • Blinding/double-blind experiment
   • Use a simulation
     • Randomization
   • Use a survey
     • Replication
   • Do an observational study
     • Confounding Variable
   • Simple Random Sample
     • Stratified sample
     • Cluster Sample
     • Systematic Sample

3. Descriptive Statistics: The branch of statistics that involves organizing and displaying the collected data.

4. Inferential Statistics: Branch of statistics that involves using a sample to draw conclusions about a population

5. Chapter 2: Descriptive Statistics

   • Frequency distribution
     • Class Limits
       • Lower
       • Upper
     • Class width
     • Range
     • Midpoint
     • Relative frequency
     • Cumulative frequency
   • Frequency polygon
   • Frequency histogram
     • Relative frequency histogram
   • Ogive
   • Graphing Quantitative Data Sets
     • Stem-and-leaf plots
       • Unordered stem-and-leaf plot
       • Ordered stem-and-leaf plot
     • Dot Plot
     • Pie Chart
     • Pareto Chart
     • Scatter Plot
     • Time Series Plot
   • Measures of Central Tendency
     • Mean: Sum of all data entries
     • Median: The value that lies in the middle of the data
     • Mode: The data entry that occurs with the greatest frequency
       • Bimodal: The data set and mode that results when two data entries occur with the same greatest frequencies
     • Outlier: A data entry that is far removed from the other entries in the data set
     • Weighted mean: Is the mean of a data set whose entries have varying weights
     • Mean of a frequency distribution
       • symmetric
       • Uniform or rectangular
       • Skewed left
       • Skewed right
   • Measures of variation
     • Range: Is the difference between maximum and minimum data entries
     • Deviation: Is the difference between the entry and the mean U of the data set
     • Population variance
     • Population standard deviation: The square root of the population variance
     • Sample variance
     • Sample standard deviation
     • The Empirical Rule
       • Chebychev's Theorem
         • Grouped Data
           • Midpoints of Classes
   • Measures of position
     • Quartiles
       • second quartile
       • third quartile
       • first quartile
     • interquartile range (IQR)
     • box-and-whisper plot
     • Percentiles
       • Deciles
     • Standard Score
       • Z-score

6. Chapter three: Probability

   • Basic Concepts of Probability and Counting
     • Probability Experiment: An action or trial where specific results are obtained
     • Outcome: The result of a single trial in a probability experiment
     • Sample space: The set of all possible outcomes of a probability experiment
     • Event: A subset of the sample space
     • Simple event: An event that consists of a single outcome
     • Fundamental Counting Principle
     • Classical/theoretical Probability
     • Empirical and Statistical Probability
     • Complement of event E
     • Tree Diagram
     • Fundamental Counting Principle
   • Conditional Probability and the Multiplication rule
     • Conditional Probability
     • Dependent and Independent events
     • The Multiplication Rule
   • The Addition Rule
     • Mutually Exclusive
     • Probabilities of Mutually Exclusive events
     • Combining Rules to Find Probabilities
   • Additional Topics in Probability and Counting
     • Permutation: An ordered arrangement of objects
       • Factorial
       • nPr
       • Distinguishable Permutations
       • Fundamental Counting Principle
       • Combinations

7. Chapter Four: Discrete Probability Distributions

   • Probability Distributions
     • Random Variable
     • Discrete
     • Continuous
     • Discrete Probability Distribution
       • Constructing and Graphing
     • Verify
     • Identify
     • Mean of Probability Distribution
       • Variance
         • Standard Deviation
     • Expected Value: Equal to the mean of the random variable
   • Binomial Distributions
     • Binomial Experiment: The probability that satisfies certain conditions
     • Binomial Probability
     • Table
     • Graphing
     • Finding and Interpreting Mean, Variance, and Standard Deviation
   • More Discrete Probability Distributions
     • Geometric Distribution: A discrete probability distribution of a random variable x that follows certain conditions
     • Poisson Distribution: Is a discrete probability distribution of a random variable x that satisfies certain conditions

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