Question

Deviation

Answer 1

@msumner

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

Do you get this?

Answer 6

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

Answer 7

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

Answer 8

NP:)
Standard deviation is the square root of variance

Answer 9

how about we establish a more concrete example?

Answer 10

@ParthKohli It's for individual element

Answer 11

I hope it is not too much to ask

Answer 12

Cool :)

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

I think I have seen this on Wikipedia.

Answer 17

Yes, I have taken the same example

Answer 18

So the variance is \(4\).

Answer 19

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

Answer 20

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

Answer 21

Do you get this?

Answer 22

@msumner

Answer 23

why do we square the differences?

Answer 24

Yup, can you tell me the formula for variance?

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

hmm

Answer 29

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

Answer 30

That is why statistics is pretty trivial.

Answer 31

Yeah, then just take the absolute value of difference

Answer 32

Will we get the same answer?

Answer 33

We'll get Absolute deviation for individual element

Answer 34

|(2−5)|=3
|(4−5)|=1
|(4−5)|=1
|(4−5)|=1
|(5−5)|=0
|(5−5)|=0
|(7−5)|=2
|(9−5)|=4

Answer 35

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

Answer 36

@ParthKohli No, we won't get the same result
Absolute deviation is defined for individual element, we won't take mean in this case

Answer 37

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

Answer 38

Average of the absolute deviation is 12/8=1.5

Answer 39

is this the same concept as the distance between points?

Answer 40

Yes!

Answer 41

Wow, I just got enlightenment.

Answer 42

@msumner do you get the insight?

Answer 43

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

Answer 44

This is somewhat like that.

Answer 45

Absolute deviation and standard deviation are different. T_T

Answer 46

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

Answer 47

Population and Sample

Answer 48

What do you want to know?

Answer 49

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

Answer 50

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

Answer 51

Let me think :)

Answer 52

I hope my questions are not a nuisance or troublesome!

Answer 53

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

Answer 54

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

Answer 55

Questions are good,

Answer 56

*samples

Answer 57

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

Answer 58

I am 13 and I have even more n00bish questions.

Answer 59

No problem:)

Answer 60

Here is what I am talking about

Answer 61

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

Answer 62

http://en.wikipedia.org/wiki/Statistical_population

and

http://en.wikipedia.org/wiki/Statistical_sample

Answer 63

@Hero

help please

Answer 64

It says that a sample is a subset of population.

Answer 65

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

Answer 66

Hero do you know what ash is talking about?

Answer 67

it will help

Answer 68

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

Answer 69

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

Answer 70

Really?

Answer 71

draw it then

Answer 72

draw then upload works!

Answer 73

now I get it. thank you!

Answer 74

I should close it, shouldn't I?

Answer 75

yes, please. Thank you once again