Deviation

- ash2326

Deviation

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- ash2326

@msumner

- ash2326

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

- ash2326

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

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## More answers

- ash2326

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

- ash2326

Do you get this?

- ParthKohli

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

- anonymous

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

- ash2326

NP:)
Standard deviation is the square root of variance

- anonymous

how about we establish a more concrete example?

- ash2326

@ParthKohli It's for individual element

- anonymous

I hope it is not too much to ask

- ash2326

Cool :)

- ParthKohli

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

- ash2326

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

- ash2326

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

- ParthKohli

I think I have seen this on Wikipedia.

- ash2326

Yes, I have taken the same example

- ParthKohli

So the variance is \(4\).

- ash2326

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

- ash2326

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

- ash2326

Do you get this?

- ash2326

@msumner

- anonymous

why do we square the differences?

- ParthKohli

Yup, can you tell me the formula for variance?

- ParthKohli

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

- ParthKohli

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

- ash2326

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

- anonymous

hmm

- anonymous

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

- ParthKohli

That is why statistics is pretty trivial.

- ash2326

Yeah, then just take the absolute value of difference

- ParthKohli

Will we get the same answer?

- ash2326

We'll get Absolute deviation for individual element

- 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

- anonymous

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

- 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

- ParthKohli

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

- ash2326

Average of the absolute deviation is 12/8=1.5

- anonymous

is this the same concept as the distance between points?

- ParthKohli

Yes!

- ParthKohli

Wow, I just got enlightenment.

- ash2326

@msumner do you get the insight?

- anonymous

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

- ParthKohli

This is somewhat like that.

- ParthKohli

Absolute deviation and standard deviation are different. T_T

- ash2326

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

- anonymous

Population and Sample

- ash2326

What do you want to know?

- anonymous

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

- anonymous

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

- ash2326

Let me think :)

- anonymous

I hope my questions are not a nuisance or troublesome!

- ParthKohli

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

- ash2326

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

- ash2326

Questions are good,

- ash2326

*samples

- anonymous

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

- ParthKohli

I am 13 and I have even more n00bish questions.

- ash2326

No problem:)

- anonymous

Here is what I am talking about

##### 1 Attachment

- ash2326

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

- ParthKohli

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

- anonymous

@Hero
help please

- ParthKohli

It says that a sample is a subset of population.

- 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

- anonymous

Hero do you know what ash is talking about?

- anonymous

it will help

- ParthKohli

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

- anonymous

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

- ParthKohli

Really?

- anonymous

draw it then

- anonymous

draw then upload works!

- anonymous

now I get it. thank you!

- ash2326

I should close it, shouldn't I?

- anonymous

yes, please. Thank you once again

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