Statistical Analysis Test 1 Definitions

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Jamie_Bee
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275010
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Statistical Analysis Test 1 Definitions
Updated:
2014-05-21 22:25:02
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Stats Definitions University
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Definitions for Statistical Analysis
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  1. Population
    The collection of all objects or elements of interest in a study
  2. Parameter
    A quantitative measure that describes a characteristic of a population
  3. Statistic
    A quantitative measure that describes a characteristic of a sample
  4. Sample
    Any portion of a population selected for study
  5. Random sample
    When each and every element in the population gets an equal chance of being selected in the sample
  6. Sampling Units
    Non-overlapping collections of elements from a population that covers the entire population
  7. Variable
    A characteristic observed on sample units that can vary from unit to unit
  8. Quantitative Variable
    A variable that can be measured numerically
  9. Qualitative Variable
    A variable that can not assume a numerical value, but can be classified into two or more categories
  10. Discrete Variable
    A variable that can assume integral values (counting numbers)
  11. Continuous Random Variable
    A variable that can assume any numberical value over a certain interval(s)
  12. The Mean
    Suppose we have a data set of sample of n-observations, say x1, x2,x3, , xn. The sample mean is denoted by x̄ and defined as x̄=
  13. The Median
    The middle number when the measurements of the data set are arranged in order from least to greatest in magnitude (a Ranked data set)
  14. The Mode
    The value(s) which occur most in a data set
  15. Quartile
    There are 3 quartiles, namely Q1, Qand Q3 which split the data set into 4 equal parts when the given data set has been ranked
  16. Percentile
    The kth percentile of a data set is denoted by Pk and defined as the value such that k% of the observations in the data set are less than or equal to that value or equivalently, (100-k)% of observations are greater than or equal to that value.
  17. Percentile Rank of Observation
    The percentage of values in the data set smaller than this value (≠)
  18. Range
    The difference between the smallest value and the largest value in the data set
  19. Sample Variance (s2)
    Suppose we have a sample of n observations, say x1, x2,x3, , xn. The sample variance is denoted by s2 and defined as the sum of the squares of the deviations of the observations in the sample from their mean.
  20. Coefficient of Variation
    Sometimes we need to compare the variability of 2 data sets that have different units of measurement
  21. Classification
    forming non-overlapping classes or intervals into which all the observations in the given data set are placed
  22. Class Limits
    The end points of each class or interval are called the class limits. The lower endpoint of the class is called the lower limit of the class, and the upper endpoint of the class is called the upper limit of the class.
  23. Class mark
    The midpoint of each class is the class mark. Therefore class mark = of the class. The class mark for the ith class is denoted by xi (book uses mi )
  24. Class Frequency
    The number of observations falling into a class. The class frequency of the ith class is denoted by fi. The sum of all the class frequencies is equal to the number of observations in the data set.
  25. Relative Frequency
    The relative frequency of the ith class is denoted by Pi and defined as Pi= , where fi is the frequency of the ith class and n is the sum of all the frequencies.
  26. Set
    A collection of well-defined objects called the elements of the set. We usually use a capital letter and curly brackets {} to denote a set.
  27. Subset
    Any part of another set is called a subset. If B is a subset of A, we write as B ⊆ A, that is whatever is in B must be in A.
  28. Empty set
    is denoted by ф and contains no elements in it
  29. Experiement
    a process by which an observation is obtained
  30. Event
    a specific collection of one or more outcome(s) of an experiment
  31. Simple Event
    An event that can't be decomposed any further
  32. Compound Event
    An event that can be decomposed into two or more simple events
  33. Sample Size
    The set of all outcomes of an experiment and is denoted by S.
  34. Probability of an Event
    The probability associated with an event A defined over the sample space S is denoted by P(A) and defined as P(A) =
  35. Union of Events
    Let A and B be any two events defined over the sample space S. The union of A and B is denoted by A∪B and defined as the set of all outcomes that are either in A or in B or in both A and B
  36. Intersection of Events
    • Let A and B be any two events defined over the sample space S. The intersection
    • of A and B is denoted by A∩B and defined as the set of all outcomes
    • which are in A and B (ie, common in A and B)
  37. Mutually Exclusive (or disjointed) Events
    Two events A an dB defined over the sample space S is said to be mutually exclusive if A∩B=ф. A∩B=ф implies that P(A∩B)=0
  38. Independent Events
    Two events A an dB defined over the sample space S is said to be independent events if A∩B=P(A)*P(B. In the case of two independent events, the occurrence of one event does not change the probability of the other.
  39. The Complement
    The complement of event A is denoted by A-bar and defined as those outcomes in the sample space S which are not in A.

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