Some Basic Concepts Schaum's Outline of Elements of Statistics I: Descriptive Statistics

1
Some Basic ConceptsSchaum's Outline of Elements
of Statistics I Descriptive Statistics
Probability
2
Chapter 1. Functions

• Function If two variables are related so that
  for every permissible specific value x of X there
  is associated one and only one specific value y
  of Y, then Y is a function of X.
• domain of the function is the set of x values
  that X can assume
• range is the set of y values associated with the
  x values
• the rule of association is the function itself

3
Chapter 1. Functions in statistics

• Independent/dependent variables and cause/effect
• In the mathematical function y f(x), y is said
  to be the dependent variable and x the
  independent variable because y depends on x
• In the research context the dependent variable is
  a measurement variable that has values that to
  some degree depend on the values of a measurement
  variable associated with the cause

4
Chapter 2. Measurement scales

• Nominal unique mutually-exclusive categories,
  meaning that a measured item is equal to some
  category or not e.g., fish being shark,
  flounder, or trout.
• Ordinal nominal plus ordered e.g., eggs are
  small, medium, or large.
• Interval ordinal plus uniform reference units
  e.g., degrees Celsius.
• Ratio interval plus absolute zero making ratios
  meaningful e.g., degrees Kelvin where 300 K is
  twice as hot as 150 K.

5
Chapter 3. Probabilities for sampling with and
without replacement

• The probability of drawing an ace from a deck of
  52 cards is P(ace) 4/52, and if the sampling is
  done with replacement, the probability of drawing
  an ace on a second try is also 4/52.
• However, if the sampling is without replacement,
  the probability of drawing the second ace is
  P(second ace) 3/51

6
Chapter 4 and 5. Frequency distributions and
graphing frequency distributions

7
Chapter 6 Measures of central tendency

• Mean or average
• Median value that divides an array of ordered
  values into two equal parts
• Mode the measurement that occurs most frequently

8
Chapter 7Measures of dispersion

• Variance and Standard Deviation
• Normal probability density function (bell shaped
  curve) 68 of the values lie within one sigma
  from the mean, and 95 within two sigma from the
  mean

9
Chapter 8Probability four interpretations

• Classical deals with idealizes situations, like
  the roll of a perfect die on a flawless surface
  having equally likely (probabilities of 1/6)
  outcomes
• Relative frequency data from experiments are
  analyzed to obtain the relative frequency of
  events
• Set theory the basis for the mathematical theory
  of probability
• Subjective in contrast to the objective
  determination of probabilities above, here the
  probabilities are determined using personal
  judgment or educated guesses

10
Chapter 9Calculating rules and counting rules

• Special addition rule - A and B are mutually
  exclusive
• General addition rule - A and B are not mutually
  exclusive
• Conditional probability
• General multiplication rule - A and B not
  independent
• Special multiplication rule - A and B independent
  
• Bayes Theorem (also known as Bayes Law)

11
Chapter 10Random variables, probability
distributions, cumulative distribution functions

• Random variable function having the sample
  space as its domain, and an association rule that
  assigns a real number to each sample point in the
  sample space, and range is the sample space of
  numbers defined by the association rule
• Discrete random variable sample space is finite
  or countably infinite
• Continuous random variable sample space is
  infinite or not countable

12
Chapter 10 (cont)

• Understand discrete and continuous probability
  distributions
• Expected value of discrete probability
  distribution
• Variance of discrete probability distribution
• Expected value of continuous probability
  distribution
• Variance of continuous probability distribution