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## #1 2014-04-22 01:41:20

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,616
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### Standard deviation

the co-efficient of co-relation between 2 variables x & y is 0.64,Their co-variance is 16.The variance of x is 9.Find the standard deviation of y series?

Sorry, I do not know what this means but a guy wants me to ask you all this question. Any help is appreciated.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #2 2014-04-22 02:19:10

bob bundy
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Registered: 2010-06-20
Posts: 7,842

### Re: Standard deviation

hi Agnishom,

Variance and standard deviation are measures of how spread out a set of data is.

If you've worked out the mean, you might be tempted to calculate the distance of each x from the mean and average these to get the average spread.  But it doesn't work because that always comes to zero, as a result of how the mean is calculated.

So square each distance instead to avoid them cancelling out and average that.  The result is called the variance.

If the numbers are all fractions then squaring tends to make the numbers smaller.  If the numbers are over 1, then squaring makes them bigger.  Either way the variance is not very representative of the actual distances you started with, so a second statistic, called the standard deviation, is found by square rooting the variance.

http://www.mathsisfun.com/data/standard-deviation.html

When you have two variables, x and y, the covariance is a way of measuring how correlated they are.  eg.  If y gets bigger as x gets bigger, the covar comes out positive.  There must be a formula connecting V[X], V[Y] and CoVar[X,Y], but I'll have to look it up.  New post on this shortly.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #3 2014-04-22 02:24:40

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,616
Website

### Re: Standard deviation

Thanks bob. I will ask that guy to come in here.

Could you please post a complete walkthrough of the problem? I do not get what the problem means

Last edited by Agnishom (2014-04-22 02:27:20)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2014-04-22 02:33:19

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,842

### Re: Standard deviation

OK, found it.

Forgot the correlation:  The correlation between two variables is a measure of how closely one varies as the other varies.

eg.  If you run you get hotter.  If you measured how hot you were after 30 seconds of running, 1 minute, 90 seconds, 2 minutes etc; using x for one variable and y for the other, then the correlation between x and y would be close to 1.  (You would probably reach a hotness limit after a while so the example is not perfect. )

eg.  If you asked students to listen to a boring lecture and rate how interested they were after 30 seconds, I minute etc, you would probably find the correlation would be close to negative 1, ie as time gets bigger the interest gets smaller.

Due to the way correlation is calculated, it is always a number between -1 and + 1.

There is a neat formula which connects all these statistics:

http://mathworld.wolfram.com/Covariance.html

As you know three of the statistics you can calculate the fourth.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #5 2014-04-22 02:34:35

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,616
Website

### Re: Standard deviation

Is standard deviation the square root of the variation?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #6 2014-04-22 02:38:51

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,842

### Re: Standard deviation

I do not get what the problem means

Variance and standard deviation are explained very well on the MIF page I gave you.

Then look at Wolfram for the definition of covariance.

You really need to do some statistics to get a good 'feel' for these calculations, but, in the final analysis, they are just numbers you can calculate from data and that's what the word 'statistics' means.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #7 2014-04-22 02:40:16

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,842

### Re: Standard deviation

Is standard deviation the square root of the variation?

Yes.

Sorry I've got to go and do some chores.  Have a look at the pages I've suggested and post back when you have another question.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #8 2014-04-22 02:46:17

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,616
Website

### Re: Standard deviation

Hi bob;

Thank You

I hate the way that person does his math

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #9 2014-04-22 05:33:01

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,842

### Re: Standard deviation

I hate the way that person does his math

?? Which person??

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Online

## #10 2014-04-22 05:42:49

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,616
Website

### Re: Standard deviation

The OP. The one who asked the question in the first place.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #11 2014-04-22 06:44:03

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,842

### Re: Standard deviation

But you are the OP?  Please try to make sense.  I've got to do more chores, so I'll be off for a while.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Online

## #12 2014-04-22 07:01:56

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,616
Website

### Re: Standard deviation

From post 1

Agnishom wrote:

Sorry, I do not know what this means but a guy wants me to ask you all this question. Any help is appreciated.

I am talking about the one who gave me this question.

He does not love math. He only wants to pass a test. (which ,I think, is a very boring reason to do math)

I am looking at those pages. I'll ask you if something is amiss.

Thanks Have a happy evening.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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