ash2326
  • ash2326
Deviation
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ash2326
  • ash2326
@msumner
ash2326
  • ash2326
Suppose the average is 5 Individual observations, say one of them is 4
ash2326
  • ash2326
There are two types of deviations 1) Standard 2) Absolute

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ash2326
  • ash2326
Absolute deviation here \[|\text{observation}-\text{average or arithmetic mean}|\] \[|5-4|=1\]
ash2326
  • ash2326
Do you get this?
ParthKohli
  • ParthKohli
Absolute deviation is for a set of data elements, correct?
anonymous
  • anonymous
sorry I misspoke earlier. I meant Variance, not arithmetic mean
ash2326
  • ash2326
NP:) Standard deviation is the square root of variance
anonymous
  • anonymous
how about we establish a more concrete example?
ash2326
  • ash2326
@ParthKohli It's for individual element
anonymous
  • anonymous
I hope it is not too much to ask
ash2326
  • ash2326
Cool :)
ParthKohli
  • ParthKohli
But it's for an individual element from a set of elements, correct?
ash2326
  • 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
  • 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
  • ParthKohli
I think I have seen this on Wikipedia.
ash2326
  • ash2326
Yes, I have taken the same example
ParthKohli
  • ParthKohli
So the variance is \(4\).
ash2326
  • ash2326
Now, we need to find the average of these values That'll be the variance \[\frac{32}{8}=4\]
ash2326
  • ash2326
Square root of this is standard deviation \[\sqrt 4=2\]
ash2326
  • ash2326
Do you get this?
ash2326
  • ash2326
@msumner
anonymous
  • anonymous
why do we square the differences?
ParthKohli
  • ParthKohli
Yup, can you tell me the formula for variance?
ParthKohli
  • ParthKohli
@msumner Because we must have a positive value, that's why.
ParthKohli
  • ParthKohli
Well... something along the lines of the above.
ash2326
  • ash2326
To find the absolute value of the difference, yes @ParthKohli is right
anonymous
  • anonymous
hmm
anonymous
  • anonymous
if the goal is to get an absolute value, why not just obtain the absolute value from the get go?
ParthKohli
  • ParthKohli
That is why statistics is pretty trivial.
ash2326
  • ash2326
Yeah, then just take the absolute value of difference
ParthKohli
  • ParthKohli
Will we get the same answer?
ash2326
  • ash2326
We'll get Absolute deviation for individual element
ash2326
  • 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
  • anonymous
I doubt we will get the same result consistently if we obtain the absolute value of the difference
ash2326
  • 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
  • ParthKohli
3 + 1 + 1 + 1 + 2 + 4 = 12
ash2326
  • ash2326
Average of the absolute deviation is 12/8=1.5
anonymous
  • anonymous
is this the same concept as the distance between points?
ParthKohli
  • ParthKohli
Yes!
ParthKohli
  • ParthKohli
Wow, I just got enlightenment.
ash2326
  • ash2326
@msumner do you get the insight?
anonymous
  • anonymous
Yes. How come there are two formulas for Standard Deviation?
ParthKohli
  • ParthKohli
This is somewhat like that.
ParthKohli
  • ParthKohli
Absolute deviation and standard deviation are different. T_T
ash2326
  • ash2326
That's average absolute deviation, the one we found earlier was standard deviation
anonymous
  • anonymous
Population and Sample
ash2326
  • ash2326
What do you want to know?
anonymous
  • anonymous
why use a different formula when the population or set of elements are larger
anonymous
  • anonymous
I misspoke again. why use a different formula when the Sample is taken from a larger population?
ash2326
  • ash2326
Let me think :)
anonymous
  • anonymous
I hope my questions are not a nuisance or troublesome!
ParthKohli
  • ParthKohli
You think your questions are nuisance? What... no!
ash2326
  • ash2326
I think standard deviation will provide a better insight of the variation of the sample,
ash2326
  • ash2326
Questions are good,
ash2326
  • ash2326
*samples
anonymous
  • anonymous
I just turned 14 so bear with my amateur math questions :(
ParthKohli
  • ParthKohli
I am 13 and I have even more n00bish questions.
ash2326
  • ash2326
No problem:)
anonymous
  • anonymous
Here is what I am talking about
ash2326
  • ash2326
Ok, I never knew this, thanks Let me find about these
ParthKohli
  • ParthKohli
http://en.wikipedia.org/wiki/Statistical_population and http://en.wikipedia.org/wiki/Statistical_sample
anonymous
  • anonymous
@Hero help please
ParthKohli
  • ParthKohli
It says that a sample is a subset of population.
ash2326
  • 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
  • anonymous
Hero do you know what ash is talking about?
anonymous
  • anonymous
it will help
ParthKohli
  • ParthKohli
The population is the whole thing, and the sample is just the data collected from a small part of it.
anonymous
  • anonymous
@ParthKohli a Sample is said to be taken from a bigger population
ParthKohli
  • ParthKohli
Really?
anonymous
  • anonymous
draw it then
anonymous
  • anonymous
draw then upload works!
anonymous
  • anonymous
now I get it. thank you!
ash2326
  • ash2326
I should close it, shouldn't I?
anonymous
  • anonymous
yes, please. Thank you once again

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