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ash2326
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@msumner
ash2326
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Suppose the average is 5
Individual observations, say one of them is 4
ash2326
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There are two types of deviations
1) Standard
2) Absolute
ash2326
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Absolute deviation here
\[|\text{observation}-\text{average or arithmetic mean}|\]
\[|5-4|=1\]
ash2326
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Do you get this?
ParthKohli
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Absolute deviation is for a set of data elements, correct?
msumner
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sorry I misspoke earlier. I meant Variance, not arithmetic mean
ash2326
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NP:)
Standard deviation is the square root of variance
msumner
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how about we establish a more concrete example?
ash2326
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@ParthKohli It's for individual element
msumner
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I hope it is not too much to ask
ash2326
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Cool :)
ParthKohli
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But it's for an individual element from a set of elements, correct?
ash2326
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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
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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
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I think I have seen this on Wikipedia.
ash2326
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Yes, I have taken the same example
ParthKohli
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So the variance is \(4\).
ash2326
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Now, we need to find the average of these values
That'll be the variance
\[\frac{32}{8}=4\]
ash2326
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Square root of this is standard deviation
\[\sqrt 4=2\]
ash2326
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Do you get this?
ash2326
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@msumner
msumner
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why do we square the differences?
ParthKohli
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Yup, can you tell me the formula for variance?
ParthKohli
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@msumner Because we must have a positive value, that's why.
ParthKohli
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Well... something along the lines of the above.
ash2326
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To find the absolute value of the difference, yes @ParthKohli is right
msumner
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hmm
msumner
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if the goal is to get an absolute value, why not just obtain the absolute value from the get go?
ParthKohli
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That is why statistics is pretty trivial.
ash2326
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Yeah, then just take the absolute value of difference
ParthKohli
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Will we get the same answer?
ash2326
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We'll get Absolute deviation for individual element
ash2326
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|(2−5)|=3
|(4−5)|=1
|(4−5)|=1
|(4−5)|=1
|(5−5)|=0
|(5−5)|=0
|(7−5)|=2
|(9−5)|=4
msumner
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I doubt we will get the same result consistently if we obtain the absolute value of the difference
ash2326
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@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
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3 + 1 + 1 + 1 + 2 + 4 = 12
ash2326
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Average of the absolute deviation is 12/8=1.5
msumner
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is this the same concept as the distance between points?
ParthKohli
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Yes!
ParthKohli
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Wow, I just got enlightenment.
ash2326
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@msumner do you get the insight?
msumner
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Yes. How come there are two formulas for Standard Deviation?
ParthKohli
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This is somewhat like that.
ParthKohli
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Absolute deviation and standard deviation are different. T_T
ash2326
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That's average absolute deviation, the one we found earlier was standard deviation
msumner
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Population and Sample
ash2326
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What do you want to know?
msumner
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why use a different formula when the population or set of elements are larger
msumner
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I misspoke again. why use a different formula when the Sample is taken from a larger population?
ash2326
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Let me think :)
msumner
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I hope my questions are not a nuisance or troublesome!
ParthKohli
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You think your questions are nuisance? What... no!
ash2326
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I think standard deviation will provide a better insight of the variation of the sample,
ash2326
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Questions are good,
ash2326
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*samples
msumner
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I just turned 14 so bear with my amateur math questions :(
ParthKohli
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I am 13 and I have even more n00bish questions.
ash2326
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No problem:)
msumner
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Here is what I am talking about
ash2326
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Ok, I never knew this, thanks
Let me find about these
msumner
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@Hero
help please
ParthKohli
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It says that a sample is a subset of population.
ash2326
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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
msumner
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Hero do you know what ash is talking about?
msumner
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it will help
ParthKohli
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The population is the whole thing, and the sample is just the data collected from a small part of it.
msumner
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@ParthKohli a Sample is said to be taken from a bigger population
ParthKohli
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Really?
msumner
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draw it then
msumner
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draw then upload works!
msumner
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now I get it. thank you!
ash2326
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I should close it, shouldn't I?
msumner
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yes, please. Thank you once again