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ash2326

  • 3 years ago

Deviation

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  1. ash2326
    • 3 years ago
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    @msumner

  2. ash2326
    • 3 years ago
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    Suppose the average is 5 Individual observations, say one of them is 4

  3. ash2326
    • 3 years ago
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    There are two types of deviations 1) Standard 2) Absolute

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

  5. ash2326
    • 3 years ago
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    Do you get this?

  6. ParthKohli
    • 3 years ago
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    Absolute deviation is for a set of data elements, correct?

  7. msumner
    • 3 years ago
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    sorry I misspoke earlier. I meant Variance, not arithmetic mean

  8. ash2326
    • 3 years ago
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    NP:) Standard deviation is the square root of variance

  9. msumner
    • 3 years ago
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    how about we establish a more concrete example?

  10. ash2326
    • 3 years ago
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    @ParthKohli It's for individual element

  11. msumner
    • 3 years ago
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    I hope it is not too much to ask

  12. ash2326
    • 3 years ago
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    Cool :)

  13. ParthKohli
    • 3 years ago
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    But it's for an individual element from a set of elements, correct?

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

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

  16. ParthKohli
    • 3 years ago
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    I think I have seen this on Wikipedia.

  17. ash2326
    • 3 years ago
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    Yes, I have taken the same example

  18. ParthKohli
    • 3 years ago
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    So the variance is \(4\).

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

  20. ash2326
    • 3 years ago
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    Square root of this is standard deviation \[\sqrt 4=2\]

  21. ash2326
    • 3 years ago
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    Do you get this?

  22. ash2326
    • 3 years ago
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    @msumner

  23. msumner
    • 3 years ago
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    why do we square the differences?

  24. ParthKohli
    • 3 years ago
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    Yup, can you tell me the formula for variance?

  25. ParthKohli
    • 3 years ago
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    @msumner Because we must have a positive value, that's why.

  26. ParthKohli
    • 3 years ago
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    Well... something along the lines of the above.

  27. ash2326
    • 3 years ago
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    To find the absolute value of the difference, yes @ParthKohli is right

  28. msumner
    • 3 years ago
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    hmm

  29. msumner
    • 3 years ago
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    if the goal is to get an absolute value, why not just obtain the absolute value from the get go?

  30. ParthKohli
    • 3 years ago
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    That is why statistics is pretty trivial.

  31. ash2326
    • 3 years ago
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    Yeah, then just take the absolute value of difference

  32. ParthKohli
    • 3 years ago
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    Will we get the same answer?

  33. ash2326
    • 3 years ago
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    We'll get Absolute deviation for individual element

  34. ash2326
    • 3 years ago
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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

  35. msumner
    • 3 years ago
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    I doubt we will get the same result consistently if we obtain the absolute value of the difference

  36. ash2326
    • 3 years ago
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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

  37. ParthKohli
    • 3 years ago
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    3 + 1 + 1 + 1 + 2 + 4 = 12

  38. ash2326
    • 3 years ago
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    Average of the absolute deviation is 12/8=1.5

  39. msumner
    • 3 years ago
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    is this the same concept as the distance between points?

  40. ParthKohli
    • 3 years ago
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    Yes!

  41. ParthKohli
    • 3 years ago
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    Wow, I just got enlightenment.

  42. ash2326
    • 3 years ago
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    @msumner do you get the insight?

  43. msumner
    • 3 years ago
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    Yes. How come there are two formulas for Standard Deviation?

  44. ParthKohli
    • 3 years ago
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    This is somewhat like that.

  45. ParthKohli
    • 3 years ago
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    Absolute deviation and standard deviation are different. T_T

  46. ash2326
    • 3 years ago
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    That's average absolute deviation, the one we found earlier was standard deviation

  47. msumner
    • 3 years ago
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    Population and Sample

  48. ash2326
    • 3 years ago
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    What do you want to know?

  49. msumner
    • 3 years ago
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    why use a different formula when the population or set of elements are larger

  50. msumner
    • 3 years ago
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    I misspoke again. why use a different formula when the Sample is taken from a larger population?

  51. ash2326
    • 3 years ago
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    Let me think :)

  52. msumner
    • 3 years ago
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    I hope my questions are not a nuisance or troublesome!

  53. ParthKohli
    • 3 years ago
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    You think your questions are nuisance? What... no!

  54. ash2326
    • 3 years ago
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    I think standard deviation will provide a better insight of the variation of the sample,

  55. ash2326
    • 3 years ago
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    Questions are good,

  56. ash2326
    • 3 years ago
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    *samples

  57. msumner
    • 3 years ago
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    I just turned 14 so bear with my amateur math questions :(

  58. ParthKohli
    • 3 years ago
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    I am 13 and I have even more n00bish questions.

  59. ash2326
    • 3 years ago
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    No problem:)

  60. msumner
    • 3 years ago
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    Here is what I am talking about

  61. ash2326
    • 3 years ago
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    Ok, I never knew this, thanks Let me find about these

  62. msumner
    • 3 years ago
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    @Hero help please

  63. ParthKohli
    • 3 years ago
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    It says that a sample is a subset of population.

  64. ash2326
    • 3 years ago
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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

  65. msumner
    • 3 years ago
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    Hero do you know what ash is talking about?

  66. msumner
    • 3 years ago
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    it will help

  67. ParthKohli
    • 3 years ago
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    The population is the whole thing, and the sample is just the data collected from a small part of it.

  68. msumner
    • 3 years ago
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    @ParthKohli a Sample is said to be taken from a bigger population

  69. ParthKohli
    • 3 years ago
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    Really?

  70. msumner
    • 3 years ago
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    draw it then

  71. msumner
    • 3 years ago
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    draw then upload works!

  72. msumner
    • 3 years ago
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    now I get it. thank you!

  73. ash2326
    • 3 years ago
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    I should close it, shouldn't I?

  74. msumner
    • 3 years ago
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    yes, please. Thank you once again

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