## ash2326 2 years ago Deviation

1. ash2326

@msumner

2. ash2326

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

3. ash2326

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

4. ash2326

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

5. ash2326

Do you get this?

6. ParthKohli

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

7. msumner

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

8. ash2326

NP:) Standard deviation is the square root of variance

9. msumner

how about we establish a more concrete example?

10. ash2326

@ParthKohli It's for individual element

11. msumner

I hope it is not too much to ask

12. ash2326

Cool :)

13. ParthKohli

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

14. ash2326

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

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

I think I have seen this on Wikipedia.

17. ash2326

Yes, I have taken the same example

18. ParthKohli

So the variance is $$4$$.

19. ash2326

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

20. ash2326

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

21. ash2326

Do you get this?

22. ash2326

@msumner

23. msumner

why do we square the differences?

24. ParthKohli

Yup, can you tell me the formula for variance?

25. ParthKohli

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

26. ParthKohli

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

27. ash2326

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

28. msumner

hmm

29. msumner

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

30. ParthKohli

That is why statistics is pretty trivial.

31. ash2326

Yeah, then just take the absolute value of difference

32. ParthKohli

Will we get the same answer?

33. ash2326

We'll get Absolute deviation for individual element

34. ash2326

|(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

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

36. ash2326

@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 + 1 + 1 + 1 + 2 + 4 = 12

38. ash2326

Average of the absolute deviation is 12/8=1.5

39. msumner

is this the same concept as the distance between points?

40. ParthKohli

Yes!

41. ParthKohli

Wow, I just got enlightenment.

42. ash2326

@msumner do you get the insight?

43. msumner

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

44. ParthKohli

This is somewhat like that.

45. ParthKohli

Absolute deviation and standard deviation are different. T_T

46. ash2326

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

47. msumner

Population and Sample

48. ash2326

What do you want to know?

49. msumner

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

50. msumner

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

51. ash2326

Let me think :)

52. msumner

I hope my questions are not a nuisance or troublesome!

53. ParthKohli

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

54. ash2326

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

55. ash2326

Questions are good,

56. ash2326

*samples

57. msumner

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

58. ParthKohli

I am 13 and I have even more n00bish questions.

59. ash2326

No problem:)

60. msumner

Here is what I am talking about

61. ash2326

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

62. ParthKohli
63. msumner

64. ParthKohli

It says that a sample is a subset of population.

65. ash2326

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

Hero do you know what ash is talking about?

67. msumner

it will help

68. ParthKohli

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

69. msumner

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

70. ParthKohli

Really?

71. msumner

draw it then

72. msumner

73. msumner

now I get it. thank you!

74. ash2326

I should close it, shouldn't I?

75. msumner

yes, please. Thank you once again