Deviation

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Deviation

Mathematics
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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

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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?
Consider a population consisting of elements 2, 4, 4, 4, 5, 5, 7, 9 Let's find the mean first \[\frac{2+4+4+4+5+5+7+9}{8}=5\]
Now, we'll find the difference of each data point from the mean and we'll square it \[(2-5)^2=9\]\[(4-5)^2=1\]\[(4-5)^2=1\]\[(4-5)^2=1\]\[(5-5)^2=0\]\[(5-5)^2=0\]\[(7-5)^2=4\]\[(9-5)^2=16\]
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
|(2−5)|=3 |(4−5)|=1 |(4−5)|=1 |(4−5)|=1 |(5−5)|=0 |(5−5)|=0 |(7−5)|=2 |(9−5)|=4
I doubt we will get the same result consistently if we obtain the absolute value of the difference
@ParthKohli No, we won't get the same result Absolute deviation is defined for individual element, we won't take mean in this case
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.
@msumner do you get the insight?
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
http://en.wikipedia.org/wiki/Statistical_population and http://en.wikipedia.org/wiki/Statistical_sample
@Hero help please
It says that a sample is a subset of population.
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
Hero do you know what ash is talking about?
it will help
The population is the whole thing, and the sample is just the data collected from a small part of it.
@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

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