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ash2326 Group Title

Deviation

  • one year ago
  • one year ago

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  1. ash2326 Group Title
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    @msumner

    • one year ago
  2. ash2326 Group Title
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    Suppose the average is 5 Individual observations, say one of them is 4

    • one year ago
  3. ash2326 Group Title
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    There are two types of deviations 1) Standard 2) Absolute

    • one year ago
  4. ash2326 Group Title
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    Absolute deviation here \[|\text{observation}-\text{average or arithmetic mean}|\] \[|5-4|=1\]

    • one year ago
  5. ash2326 Group Title
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    Do you get this?

    • one year ago
  6. ParthKohli Group Title
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    Absolute deviation is for a set of data elements, correct?

    • one year ago
  7. msumner Group Title
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    sorry I misspoke earlier. I meant Variance, not arithmetic mean

    • one year ago
  8. ash2326 Group Title
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    NP:) Standard deviation is the square root of variance

    • one year ago
  9. msumner Group Title
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    how about we establish a more concrete example?

    • one year ago
  10. ash2326 Group Title
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    @ParthKohli It's for individual element

    • one year ago
  11. msumner Group Title
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    I hope it is not too much to ask

    • one year ago
  12. ash2326 Group Title
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    Cool :)

    • one year ago
  13. ParthKohli Group Title
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    But it's for an individual element from a set of elements, correct?

    • one year ago
  14. ash2326 Group Title
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    Consider a population consisting of elements 2, 4, 4, 4, 5, 5, 7, 9 Let's find the mean first \[\frac{2+4+4+4+5+5+7+9}{8}=5\]

    • one year ago
  15. ash2326 Group Title
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    Now, we'll find the difference of each data point from the mean and we'll square it \[(2-5)^2=9\]\[(4-5)^2=1\]\[(4-5)^2=1\]\[(4-5)^2=1\]\[(5-5)^2=0\]\[(5-5)^2=0\]\[(7-5)^2=4\]\[(9-5)^2=16\]

    • one year ago
  16. ParthKohli Group Title
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    I think I have seen this on Wikipedia.

    • one year ago
  17. ash2326 Group Title
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    Yes, I have taken the same example

    • one year ago
  18. ParthKohli Group Title
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    So the variance is \(4\).

    • one year ago
  19. ash2326 Group Title
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    Now, we need to find the average of these values That'll be the variance \[\frac{32}{8}=4\]

    • one year ago
  20. ash2326 Group Title
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    Square root of this is standard deviation \[\sqrt 4=2\]

    • one year ago
  21. ash2326 Group Title
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    Do you get this?

    • one year ago
  22. ash2326 Group Title
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    @msumner

    • one year ago
  23. msumner Group Title
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    why do we square the differences?

    • one year ago
  24. ParthKohli Group Title
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    Yup, can you tell me the formula for variance?

    • one year ago
  25. ParthKohli Group Title
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    @msumner Because we must have a positive value, that's why.

    • one year ago
  26. ParthKohli Group Title
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    Well... something along the lines of the above.

    • one year ago
  27. ash2326 Group Title
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    To find the absolute value of the difference, yes @ParthKohli is right

    • one year ago
  28. msumner Group Title
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    hmm

    • one year ago
  29. msumner Group Title
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    if the goal is to get an absolute value, why not just obtain the absolute value from the get go?

    • one year ago
  30. ParthKohli Group Title
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    That is why statistics is pretty trivial.

    • one year ago
  31. ash2326 Group Title
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    Yeah, then just take the absolute value of difference

    • one year ago
  32. ParthKohli Group Title
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    Will we get the same answer?

    • one year ago
  33. ash2326 Group Title
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    We'll get Absolute deviation for individual element

    • one year ago
  34. ash2326 Group Title
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    |(2−5)|=3 |(4−5)|=1 |(4−5)|=1 |(4−5)|=1 |(5−5)|=0 |(5−5)|=0 |(7−5)|=2 |(9−5)|=4

    • one year ago
  35. msumner Group Title
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    I doubt we will get the same result consistently if we obtain the absolute value of the difference

    • one year ago
  36. ash2326 Group Title
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    @ParthKohli No, we won't get the same result Absolute deviation is defined for individual element, we won't take mean in this case

    • one year ago
  37. ParthKohli Group Title
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    3 + 1 + 1 + 1 + 2 + 4 = 12

    • one year ago
  38. ash2326 Group Title
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    Average of the absolute deviation is 12/8=1.5

    • one year ago
  39. msumner Group Title
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    is this the same concept as the distance between points?

    • one year ago
  40. ParthKohli Group Title
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    Yes!

    • one year ago
  41. ParthKohli Group Title
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    Wow, I just got enlightenment.

    • one year ago
  42. ash2326 Group Title
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    @msumner do you get the insight?

    • one year ago
  43. msumner Group Title
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    Yes. How come there are two formulas for Standard Deviation?

    • one year ago
  44. ParthKohli Group Title
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    This is somewhat like that.

    • one year ago
  45. ParthKohli Group Title
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    Absolute deviation and standard deviation are different. T_T

    • one year ago
  46. ash2326 Group Title
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    That's average absolute deviation, the one we found earlier was standard deviation

    • one year ago
  47. msumner Group Title
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    Population and Sample

    • one year ago
  48. ash2326 Group Title
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    What do you want to know?

    • one year ago
  49. msumner Group Title
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    why use a different formula when the population or set of elements are larger

    • one year ago
  50. msumner Group Title
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    I misspoke again. why use a different formula when the Sample is taken from a larger population?

    • one year ago
  51. ash2326 Group Title
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    Let me think :)

    • one year ago
  52. msumner Group Title
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    I hope my questions are not a nuisance or troublesome!

    • one year ago
  53. ParthKohli Group Title
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    You think your questions are nuisance? What... no!

    • one year ago
  54. ash2326 Group Title
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    I think standard deviation will provide a better insight of the variation of the sample,

    • one year ago
  55. ash2326 Group Title
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    Questions are good,

    • one year ago
  56. ash2326 Group Title
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    *samples

    • one year ago
  57. msumner Group Title
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    I just turned 14 so bear with my amateur math questions :(

    • one year ago
  58. ParthKohli Group Title
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    I am 13 and I have even more n00bish questions.

    • one year ago
  59. ash2326 Group Title
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    No problem:)

    • one year ago
  60. msumner Group Title
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    Here is what I am talking about

    • one year ago
  61. ash2326 Group Title
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    Ok, I never knew this, thanks Let me find about these

    • one year ago
  62. ParthKohli Group Title
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    http://en.wikipedia.org/wiki/Statistical_population and http://en.wikipedia.org/wiki/Statistical_sample

    • one year ago
  63. msumner Group Title
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    @Hero help please

    • one year ago
  64. ParthKohli Group Title
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    It says that a sample is a subset of population.

    • one year ago
  65. ash2326 Group Title
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    Population is used when we have data for all the population if we have data only for a sample of population, we use the sample standard deviation to guess estimate for the whole population

    • one year ago
  66. msumner Group Title
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    Hero do you know what ash is talking about?

    • one year ago
  67. msumner Group Title
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    it will help

    • one year ago
  68. ParthKohli Group Title
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    The population is the whole thing, and the sample is just the data collected from a small part of it.

    • one year ago
  69. msumner Group Title
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    @ParthKohli a Sample is said to be taken from a bigger population

    • one year ago
  70. ParthKohli Group Title
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    Really?

    • one year ago
  71. msumner Group Title
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    draw it then

    • one year ago
  72. msumner Group Title
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    draw then upload works!

    • one year ago
  73. msumner Group Title
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    now I get it. thank you!

    • one year ago
  74. ash2326 Group Title
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    I should close it, shouldn't I?

    • one year ago
  75. msumner Group Title
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    yes, please. Thank you once again

    • one year ago
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