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Flashcards

Distributions

megan trent English 46 cards

Distributions

Cards in this deck (46)

  1. 1Distributions Why do we need this?To describe/analyse data in an appropriate way
    • To exclude human perception of the data
    • Assess differences in samples of populations
    – Assess the probability of these populations either
    being the same (“null hypothesis”), or being different
    (“Alternate hypothesis”)
    • As in life, there is no certainty resulting from statistical tests, only chance or probability.
  2. 2What is ‘Probability’?How frequently we
    expect different
    outcomes to occur if we
    repeat the experiment
    over and over…
  3. 3Definitions - variable There are two main types of data or variables:• Qualitative/categorical variables is data that is not given numerically
    e.g. gender, place of birth, type of car etc.
    • Quantitative data is numerical and are two types:
    1. Discrete data – which can only take specific numeric values;
    e.g. shoe size, number of brothers, number of cars
    2. Continuous data – can take any numerical values;
    e.g. height, mass, length, time etc.
  4. 4Let look at discreate data and a frequency distributionLet look at discreate data and a frequency distribution
  5. 5Probability distributionProbability distribution
  6. 6What about continuous variables?Time for Lecturer A to respond to emails (in
    hours and minutes):
    Problem: time to respond is a continuous
    variable and not two times will be the same!
    A ‘frequency distribution’ will be useless as we would have 50 odd times each with a
    frequency of 1.
    The solution to this problem is a ‘grouped frequency distribution’
  7. 7What about continuous variable Time for Lecturer A to respond to emails (in hours and minutes):What about continuous variable Time for Lecturer A to respond to emails (in hours and minutes):
  8. 8Continuous variables – grouped frequency distributionContinuous variables – grouped frequency distribution
  9. 9Examining a DistributionCentral tendency is measured in three ways:
    – mean, median and mode.
    • Mean - average score of a distribution.
    • Median is the centre, or middle score within a distribution.
    • Mode is the most frequent score within a distribution.
  10. 10Measures of Central Tendency Number of mobile numbers on students’ mobile phones Student # of NumbersMeasures of Central Tendency Number of mobile numbers on students’ mobile phones Student # of Numbers
  11. 11Calculating mean, median and modeCalculating mean, median and mode
  12. 12—yesyes
  13. 13In a normal distributionMean= median=mode
  14. 14The Gaussian (aka ‘normal’) distribution• Distributions for continuous variables are called continuous distributions (probability densities)
    • Some probability densities have particular importance in statistics. A very important one is shaped like a bell, and
    called the normal distribution
    • Many naturally-occurring phenomena can be approximated surprisingly well by this distribution
  15. 15The ‘normal distribution’The area under the curve equals 1
    • The probability of any exact value
    of X is 0
    • The area under the curve between
    two given points on the X-axis is
    the probability that a number
    chosen at random will fall between
    the two points
    Varying the Parameters σ and μ, we obtain
    Different Normal Distributions.
  16. 16The Mathematical ModelThe Mathematical Model
  17. 17The Mathematical ModelThe Mathematical Model
  18. 18Finding ProbabilitiesP(c ≤ X ≤ d ) = ?
    Probability is the
    area under the
    curve!
  19. 19Finding ProbabilitiesFinding Probabilities
  20. 20What is the Standard Deviation?Standard Deviation is a measure of variability or scatter around a meanWhat is the Standard Deviation?
  21. 21What is the Standard Deviation?What is the Standard Deviation?
  22. 22Normal DistributionA symmetric distribution defined on the range -∞to + ∞ whose shape is
    defined by two parameters, the mean, denoted σ, that centers the
    distribution, and the standard deviation, , that determines the spread
    of the distribution.
  23. 23Normal DistributionNormal Distribution
  24. 24Standard deviations – spread of data Normal distributionStandard deviations – spread of data Normal distribution
  25. 25Application of the normal distribution – example 1A certain type of storages battery lasts, on average, 3.0 years, with a standard derivation of 0.5 year.
    Assuming that the battery lives are normally distributed, find the probability that a given battery will last LESS than 2.3 years
  26. 26Application of the normal distribution – example 1Application of the normal distribution – example 1
  27. 27Standardized normal variableIt would be difficult and tedious to do the calculus every time we had a new set of parameters for µ and σ. So instead, we usually work with the standardized normal distribution, where µ = 0 and σ = 1
    The normal random variable of a standard normal
    distribution is called a standard score or a z-score. Every
    normal random variable X can be transformed into a z score via the following equation:
  28. 28Standardized normal variable Every normal random variable X can be transformed into a z score via the following equation:Standardized normal variable Every normal random variable X can be transformed into a z score via the following equation:
  29. 29Standard Normal Distributionthe standard normal distribution is a special case of the normal
    distribution. It is the distribution that occurs when a normal random
    variable has a mean of zero and a standard
    deviation of one.
  30. 30Standard Normal DistributionStandard Normal Distribution
  31. 31Application of the normal distribution – example 1A certain type of storages battery lasts, on average, 3.0 years, with a standard derivation of 0.5 year. Assuming that the battery lives are normally distributed, find the probability that a given battery will last LESS than 2.3 years
  32. 32Application of the normal distribution – example 1Application of the normal distribution – example 1
  33. 33Application of the normal distribution – example 1Application of the normal distribution – example 1
  34. 34table of standard probabilitiestable of standard probabilities
  35. 35Application of the normal distribution – example 3The averages life expectancy in UK is 81
    years old with a standard derivation of 10
    years. Assuming that life expectancy is
    normally distributed, find the probability
    that you will live above 90 year old?
  36. 36Application of the normal distribution – example 3The average mark for the BIOT1004 module is 75 marks with a standard derivation of 14.2. Assuming that the mark distribution is normally distributed, find the probability that a student will get a mark between 50-60?
  37. 37Application of the normal distribution – example 3Application of the normal distribution – example 3
  38. 38Anytime that you are performing a statistical analysis (t-test, ANOVA and many more), you need tomake sure that you are working
    with normally distributed data, or your
    analysis will probably not be valid
  39. 39back to the example ‘response time’ Is this distribution ‘normal’?back to the example ‘response time’ Is this distribution ‘normal’?
  40. 40Skewness negatively skewedSkewness negatively skewed
  41. 41Skewness normal (no skew)Skewness normal (no skew)
  42. 42Skewness positively skewedSkewness positively skewed
  43. 43Looking at symmetry Skewnessthe level of non-symmetry. A
    symmetric dataset got a skewness of 0
  44. 44Looking at symmetry Kurtosisa measure of the combined
    weight of the tails relative to the rest of
    the distribution’. Normally distributed data got a value of 0
  45. 45Looking at symmetryLooking at symmetry
  46. 46—

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Flashcards on Distributions, created by megan trent on 06/10/2020.
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megan trent
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