Stat & Prob ch 2

  1. Data Range
    The difference between the maximum and minimum member of a data set.
  2. Class Width
    The difference between the lower (or upper) limits of two adjacent classes.
  3. Class boundary
    The midpoint of the interval between the upper limit of a class and the lower limit of the next class
  4. Class midpoint
    The midpoint of the interval between the lower and upper limits of a class.
  5. Class frequency
    The number of scores that fall in a class.
  6. Relative frequency
    The number of scores that fall in a class
  7. Cumulative frequency
    The sum of frequencies for a specific class and all classes below it.
  8. Frequency histogram
    A bar diagram where each bar corresponds to one of the classes, and its height is equal to class' frequency (to some scale).
  9. Ogive
    a Graph of cumulative frequency distribution
  10. Pie chart
    A circular diagram depicting the distribution of qualitative data.
  11. Center
    A representative or average value that indicates where the middle of the data set is located.
  12. Variation
    A measure of the amount that the data values vary.
  13. Distribution
    The nature or shape of the spread of the data over the range of values (such as bell-shapred, uniform, or skewed).
  14. Outliers
    Sample values that lie very far away from the vast majority of the other sample values.
  15. Time
    Changing characteristics of the data over time
  16. CVDOT
    Center, Variation, Distribution, Outliers, Time
  17. Class width=
    • (maximum data value) - (Minimum data value)
    • Number of classes
  18. The number of classes should be between
    5 & 20
  19. Relative frequency=
    • class frequency
    • sum of all frequencies
  20. Percentage frequency =
    • Class frequency
    • sum of all frequency x 100%
  21. Mean
    The average value of all members of a data set
  22. Sample mean:
    Image Upload 1
  23. Population Mean
    Image Upload 2
  24. Median
    The middle value of a data set that is arranged in ascending or descending order.
  25. Mode
    The value most frequently occurring in a data set.
  26. Midrange
    The half-sum of the minimum and maximum value of a data set.
  27. Weighted Mean
    The mean of a data set whose members have a different significance (weight) w:

    Image Upload 3
  28. Skewness
    The measure of a distribution’s asymmetry. (A left-skewed distribution has a peak shifted to the right, and vice versa.)
  29. Standard deviation
    A measure of variation taking into account each member of a data set.
  30. Population standard deviation
    Image Upload 4
  31. Sample standard deviation
    Image Upload 5
  32. Coefficient of variation (CV)
    A relative measure of variation.

    Image Upload 6
  33. z- score (standardized value)
    • A measure of relative standing, showing how many standard deviations the given value is below or
    • above the mean.

    Image Upload 7
  34. Unusually small or unusually large values
    Any values that are more than two standard deviations below or above the mean.
  35. Quartiles
    Characteristic values dividing a data set (arranged in ascending/descending order) in quarters.
  36. Interquartile range (IQR)
    The difference between the third and the first quartile.
  37. Outlier
    An extremely small or extremely large value in a data set.
  38. Sigma
    demotes the sum of a set of data values
  39. x
    is the variable usually used to represent the individual data values.
  40. n
    represents the number of data values in a sample
  41. N
    represents the number of data values in a populations.
  42. Probability experiment
    An action involving uncertainty and consisting of a number of trials for which an outcome (measurement, response etc.) is obtained.
  43. Sample space
    The set of all possible outcomes of an experiment.
  44. Event
    A collection of outcomes.
  45. Simple event
    An event that includes just one outcome.
  46. Compound event
    An event that includes two or more outcomes.
  47. Probability Rule 1 (Relative Frequency Approximation)
    If the experiment was performed m times and event A occurred f times, then the probability of event A is

    Image Upload 8
  48. Probability Rule 2 (Classical Approach)
    • If the number of simple events (sample space size) is n and the number of ways the event A can occur is s, then
    • the probability of event A is

    Image Upload 9
  49. Subjective probability
    A probability that is based on intuitive feeling rather than on logical reasoning.
  50. Law of Large Numbers
    The larger is the number of trials, the closer is the probability by Rule 1 to the actual probability.
  51. Range of probability
    The probability of an event may be a number in the interval from 0 to 1 inclusive.

    The probability of an impossible event is 0.

    The probability of an event that is certain to occur is 1.
  52. Complementary events
    Two events such that one or the other must occur, but not both at the same time.
  53. Formal Addition Rule
    The probability that either event A occurs, or event B occurs, or both occur at the same time is

    P(A or B) = P(A) + P(B) – P(A and B)

    • where P(A and B) is the probability that both A and
    • B occur at the same time.
  54. Mutually exclusive (disjoint) events
    Two events that cannot occur at the same time.
  55. Addition Rule for mutually exclusive events
    P(A or B) = P(A) + P(B)
  56. Rule of Complementary Events
    • If two events A and are complementary, then
    • Image Upload 10
  57. Conditional probability (probability of B given A)
    • The probability of event B occurring under condition
    • that event A has occurred.
  58. Independent events
    Two event (A and B) such that the probability of B does not depend on whether A occurred or not.
  59. Formal Multiplication Rule
    • The probability of events A and B occurring consequently is
    • P(A and B) = P(A)×P(B½A)
  60. Multiplication Rule for independent events
    P(A and B) = P(A)×P(B)
  61. Rule of At Least One
    P (at least 1) = 1 – P(0)
  62. Fundamental Counting Rule
    • If a procedure consists of two events, such that one can occur in m ways and the other in n ways,
    • the whole procedure can occur in m·n ways.

    The same principal is applicable to a procedure consisting of more than two events.
  63. Factorial function
    The product Image Upload 11 = n! is called n factorial.

    This definition applies to n> 1. 0! = 1.
  64. Permutation Rule (when all items are different)
    The number of ways r items can be selected from a set of n items (r < n) and arranged in all possible orders is

    • Image Upload 12
    • Another form of this formula:
  65. Factorial Rule
    n different items can be arranged in n! ways.
  66. Combination Rule
    • The number of ways r items can be selected
    • from a set of n items (r < n) is

    Image Upload 13
Card Set
Stat & Prob ch 2
Statistics and Probability chapter 2 lecture