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

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

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

Do you get this?

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

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

NP:)
Standard deviation is the square root of variance

how about we establish a more concrete example?

@ParthKohli It's for individual element

I hope it is not too much to ask

Cool :)

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

I think I have seen this on Wikipedia.

Yes, I have taken the same example

So the variance is \(4\).

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

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

Do you get this?

why do we square the differences?

Yup, can you tell me the formula for variance?

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

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

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

hmm

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

That is why statistics is pretty trivial.

Yeah, then just take the absolute value of difference

Will we get the same answer?

We'll get Absolute deviation for individual element

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

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

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

Average of the absolute deviation is 12/8=1.5

is this the same concept as the distance between points?

Yes!

Wow, I just got enlightenment.

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

This is somewhat like that.

Absolute deviation and standard deviation are different. T_T

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

Population and Sample

What do you want to know?

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

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

Let me think :)

I hope my questions are not a nuisance or troublesome!

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

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

Questions are good,

*samples

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

I am 13 and I have even more n00bish questions.

No problem:)

Here is what I am talking about

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

It says that a sample is a subset of population.

Hero do you know what ash is talking about?

it will help

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

Really?

draw it then

draw then upload works!

now I get it. thank you!

I should close it, shouldn't I?

yes, please. Thank you once again