[11] Stats and Prob - Definition of Terms

• Statistics - science of collecting, describing, and interpreting data
• Two Areas of Statistics

  • Descriptive
  • Inferential
• Descriptive Statistics - provides information only about the collected data and in no way draws inferences
• Two Types of Descriptive Statistics

  • Measures of Central Tendency
  • Measures of Spread
• Measures of Central Tendency - calculated and expressed as the mean, median, and mode
• Measures of Spread - how the data are distributed and how they relate to each other (frequency distribution, quartiles, mean absolute deviation, variance, standard deviation)
• Inferential Statistics - methods concerned with the analysis of a subset of data; decisions about a statistical population are made based only one a sample having been observed or a judgment having been obtained
• Two Types of Problems of Inferential Statistics

  • Estimation of Population Parameters
  • Tests of Hypothesis
• Population - collection, or set, of individuals or objects of events whose properties are to be analyzed
• Two Kinds of Population

  • Finite
  • Infinite
• Sample - subset of the population
• Variable - characteristic about each individual element of a population or sample
• Data (Singular) - value of the variable associated with one element of a population or sample; value may be a number, word, or symbol
• Data (Plural) - set of values collected for the variable from each other elements belonging to the sample
• Experiment - planned activity whose results yield a set of data
• Parameter - numerical value summarizing all the data of an entire population
• Statistic - numerical value summarizing the sample data
• Two Kinds of Variables

  • Qualitative, or Attribute, or Categorical, Variable
  • Quantitative, or Numerical, Variable
• Qualitative, or Attribute, or Categorical, Variable - variable that categorizes or describes an element of a population
• Quantitative, or Numerical, Variable - variable that quantifies an element of a population
• Nominal Variable - qualitative variable that categorizes (or describes, or names) an element of a population
• Ordinal Variable - qualitative variable that incorporates an ordered position, or ranking
• Discrete Variable - quantitative variable that can assume a countable number of values
• Continuous Variable - quantitative variable that can assume an uncountable number of values
• Classical Probability - possible outcome of any event in a classical manner
• Empirical Probability - uses the number of occurrences of a given outcome within the sample set
• Subjective Probability - based on educated guess or estimate (statistical treatment)
• Probability Distribution - refers to the arrangement of values of a random variable and the probabilities assigned to them