Statistics & Probability

• Statistics 


  Science that studies data to be able to make a decision
• Statistics


  tool in decision-making process
• 2 categories of statistics

  • Descriptive Statistics
  • Inferential Statistics
• Descriptive Statistics


  Uses data to provide descriptions about a population; usually numerical calculations or table/graph; information about a certain sample/population
• Inferential Statistics

  Makes predictions or conclusions about a population based on the sample of data taken from the population
• Data


  facts or figures collected on some characteristics of a sample/population
• Population


  totality of observation with which we are concerned
• Sample


  subset of a population
• Parameter


  one characteristic about a population
• Estimate


  measure of a sample, considering a population
• Types of Questions

  • Statistical Questions
  • Non-statistical Questions
• Statistical Questions


  answered by collecting data with variation; usually done through a survey/research
• Non-statistical Questions


  answers requires specific facts
• Examples of Statistical Questions

  • What is the most favourable color among teenagers?
  • How much is your monthly salary?
  • What is the ideal age to get married?
• Examples of Non-Statistical Questions

  • What is your name?
  • What is the title of our National Anthem?
• Probability

  
• Properties of Probability

  
• Examples of Probability

  • Tossing a coin
  • Throwing a dice
  • Drawing from a deck of cards
• Probability Histogram


  This is the graph that display possible values of a discrete random variable on the horizontal axis and the probabilities of those values on the vertical axis
• Random Variable


  Is a numerical quantity that is assigned to the outcome of anexperiment.
• Quantitative Variable


  assumes numerical values associated with the events of an experiment.
• Qualitative Variables


  generates categorical data; also called as Categorical Variables as it allows classification of individuals based on some attribute or characteristics
• Quantitative Variables


  generates numerical data; Arithmetic operations such as addition and subtraction can be performed on the values and provide meaningful results.
• Quantitative Variables

  • Height
  • Number of sibling(s)
  • speed of a car
  • temperature
• Qualitative variables

  • color
  • taste
  • occupation
  • gender
• Classification of Quantitative Variable

  • Discrete Random Variable
  • Continuous Random Variable
• Discrete Random Variable


  set of possible outcomes is countable, therefore represents count data (signal word - "number of...")
• Discrete Random Variable


  variables can assume only a finite or specific number of values
• Continuous Random Variable


  takes on values on continuous scale, therefore represents measured data (height, weight, temperature, time, speed, area)
• Continuous Random Variable


  variables can assume an infinite number of values within a specific interval
• Random Variable


  a function that associates a real number with each element in the sample space; it is a variable whose values are determined by chance
• Random Variable


  a numerical quantity that is derived from the outcomes of a randomexperiment
• Statistical Levels of Measurement

  • Nominal scale - data can only be categorized
  • Ordinal scale - data can be categorized and ranked
  • Interval Scale - data can be categorized, ranked, and evenly space
  • Ratio scale - data can be categorized, ranked, evenly spaced, and has a natural zero
• Sample space


  collection or set of possible outcomes of a random experiment. Represented by the symbol, "S". May contain a number of outcomes depending on the research.
• Events


  subset of possible outcomes of a random experiment
• Steps in frequency distribution and possible outcomes

  • List down sample space of the experiment; e.g. S = {xx, yy, xy, yx}
  • Count the number of the random variable (e.g. X) in each outcome and assign this number to this outcome
  • Construct frequency distribution of the values of the random variable X
  • Construct the probability distribution of the random variableX by getting the probability of occurrence of each value of therandom variable.