ash2326 Group Title Deviation one year ago one year ago

1. ash2326 Group Title

@msumner

2. ash2326 Group Title

Suppose the average is 5 Individual observations, say one of them is 4

3. ash2326 Group Title

There are two types of deviations 1) Standard 2) Absolute

4. ash2326 Group Title

Absolute deviation here $|\text{observation}-\text{average or arithmetic mean}|$ $|5-4|=1$

5. ash2326 Group Title

Do you get this?

6. ParthKohli Group Title

Absolute deviation is for a set of data elements, correct?

7. msumner Group Title

sorry I misspoke earlier. I meant Variance, not arithmetic mean

8. ash2326 Group Title

NP:) Standard deviation is the square root of variance

9. msumner Group Title

how about we establish a more concrete example?

10. ash2326 Group Title

@ParthKohli It's for individual element

11. msumner Group Title

I hope it is not too much to ask

12. ash2326 Group Title

Cool :)

13. ParthKohli Group Title

But it's for an individual element from a set of elements, correct?

14. ash2326 Group Title

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 Group Title

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 Group Title

I think I have seen this on Wikipedia.

17. ash2326 Group Title

Yes, I have taken the same example

18. ParthKohli Group Title

So the variance is $$4$$.

19. ash2326 Group Title

Now, we need to find the average of these values That'll be the variance $\frac{32}{8}=4$

20. ash2326 Group Title

Square root of this is standard deviation $\sqrt 4=2$

21. ash2326 Group Title

Do you get this?

22. ash2326 Group Title

@msumner

23. msumner Group Title

why do we square the differences?

24. ParthKohli Group Title

Yup, can you tell me the formula for variance?

25. ParthKohli Group Title

@msumner Because we must have a positive value, that's why.

26. ParthKohli Group Title

Well... something along the lines of the above.

27. ash2326 Group Title

To find the absolute value of the difference, yes @ParthKohli is right

28. msumner Group Title

hmm

29. msumner Group Title

if the goal is to get an absolute value, why not just obtain the absolute value from the get go?

30. ParthKohli Group Title

That is why statistics is pretty trivial.

31. ash2326 Group Title

Yeah, then just take the absolute value of difference

32. ParthKohli Group Title

Will we get the same answer?

33. ash2326 Group Title

We'll get Absolute deviation for individual element

34. ash2326 Group Title

|(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 Group Title

I doubt we will get the same result consistently if we obtain the absolute value of the difference

36. ash2326 Group Title

@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 Group Title

3 + 1 + 1 + 1 + 2 + 4 = 12

38. ash2326 Group Title

Average of the absolute deviation is 12/8=1.5

39. msumner Group Title

is this the same concept as the distance between points?

40. ParthKohli Group Title

Yes!

41. ParthKohli Group Title

Wow, I just got enlightenment.

42. ash2326 Group Title

@msumner do you get the insight?

43. msumner Group Title

Yes. How come there are two formulas for Standard Deviation?

44. ParthKohli Group Title

This is somewhat like that.

45. ParthKohli Group Title

Absolute deviation and standard deviation are different. T_T

46. ash2326 Group Title

That's average absolute deviation, the one we found earlier was standard deviation

47. msumner Group Title

Population and Sample

48. ash2326 Group Title

What do you want to know?

49. msumner Group Title

why use a different formula when the population or set of elements are larger

50. msumner Group Title

I misspoke again. why use a different formula when the Sample is taken from a larger population?

51. ash2326 Group Title

Let me think :)

52. msumner Group Title

I hope my questions are not a nuisance or troublesome!

53. ParthKohli Group Title

You think your questions are nuisance? What... no!

54. ash2326 Group Title

I think standard deviation will provide a better insight of the variation of the sample,

55. ash2326 Group Title

Questions are good,

56. ash2326 Group Title

*samples

57. msumner Group Title

I just turned 14 so bear with my amateur math questions :(

58. ParthKohli Group Title

I am 13 and I have even more n00bish questions.

59. ash2326 Group Title

No problem:)

60. msumner Group Title

Here is what I am talking about

61. ash2326 Group Title

Ok, I never knew this, thanks Let me find about these

62. ParthKohli Group Title
63. msumner Group Title

64. ParthKohli Group Title

It says that a sample is a subset of population.

65. ash2326 Group Title

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

66. msumner Group Title

Hero do you know what ash is talking about?

67. msumner Group Title

it will help

68. ParthKohli Group Title

The population is the whole thing, and the sample is just the data collected from a small part of it.

69. msumner Group Title

@ParthKohli a Sample is said to be taken from a bigger population

70. ParthKohli Group Title

Really?

71. msumner Group Title

draw it then

72. msumner Group Title

73. msumner Group Title

now I get it. thank you!

74. ash2326 Group Title

I should close it, shouldn't I?

75. msumner Group Title

yes, please. Thank you once again