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What is Variance?

SBS1984E
27 Jun 09, 00:34

Qn: 93 metal bars are manufactured by one machine. The length, x in metres, of each of the bars, is recorded.
The results are as follows: ∑x=102.4 and ∑x^2= â€Šâ€Š329.11

Based on the given question, how do I calculate the Variance and what does it mean?

The formula I have is

[ ∑ ( x_i - x*)^2] / n

x* = Mean of x. Dunno how to type it.
charlize
27 Jun 09, 00:44

I think u need to expand the formula above and then sub in the values.
charlize
27 Jun 09, 00:45

You can start by calculating the mean which is 102.4 / 93
SBS1984E
27 Jun 09, 01:19

But how do I get the values from ∑x=102.4 and ∑x^2= â€Šâ€Š329.11 only? The mean I calculated as 1.10m, then how do I proceed?
charlize
27 Jun 09, 01:33

You know how to expand the formula?

You will get [(x_i)^2 - 2(x_i)(x*) + (x*)^2] / n

Use ∑x=102.4 and ∑x^2= â€Šâ€Š329.11 and somehow try to sub it into the equation together with the mean u found.
charlize
27 Jun 09, 01:38

My mind is a bit groggy.

But I think it should be something like this.

Maybe can get the experts to explain clearer to u.
marcteng
27 Jun 09, 01:40

Originally posted by charlize:

My mind is a bit groggy.

But I think it should be something like this.

Maybe can get the experts to explain clearer to u.

are you maths expert lol
charlize
27 Jun 09, 01:46

Originally posted by marcteng:

are you maths expert lol

Do I sound like a math expert?

Like the rest of you, I have problems finishing my homework too.
wee_ws
27 Jun 09, 11:28

Hi SBS1984E,

Variance refers to the average of the squares of the differences between x and x-bar, as you may observe from the formula. It looks at the spread of observations of x from the mean x-bar.

What measure are you calculating, is it sample variance or the unbiased estimate of the population variance?

Given the sum of x and x^2 in the problem, the formula you have is certainly not appropriate. Do look up your notes on another equivalent formula that involves the sum of x and x^2.

Thanks!

Cheers,
Wen Shih
lianamaster
27 Jun 09, 11:29

Originally posted by SBS1984E:

Qn: 93 metal bars are manufactured by one machine. The length, x in metres, of each of the bars, is recorded.
The results are as follows: ∑x=102.4 and ∑x^2= â€Šâ€Š329.11

Based on the given question, how do I calculate the Variance and what does it mean?

The formula I have is

[ ∑ ( x_i - x*)^2] / n

x* = Mean of x. Dunno how to type it.

Variance is the square of standard deviation.

I believe the qn is on sample variance.

Since ∑x=102.4, the mean, x* = 102.4 / 93 = 1.10

Since [ ∑( x_i - x*)^2] / n = [∑( x_i)^2] / n - (x*) ^2

Variance = 329.11/93 - (1.10)(1.10) = 2.33

That's what I think...
eagle
27 Jun 09, 12:00

${}\operatorname{Var}(X)= \operatorname{E}(X^2 - 2\,X\,\operatorname{E}(X) + (\operatorname{E}(X))^2),$

${}=\operatorname{E}(X^2) - 2(\operatorname{E}(X))^2 + (\operatorname{E}(X))^2,$

${}=\operatorname{E}(X^2) - (\operatorname{E}(X))^2.$
eagle
27 Jun 09, 12:02

Also standard deviation formula from wiki is

$\sigma = \sqrt{\frac{1}{N} \left(\left(\sum_{i=1}^N x_i^2 ight) - N\overline{x}^2 ight)} = \sqrt{\frac{1}{N} \left(\sum_{i=1}^N x_i^2 ight) - \overline{x}^2}.$
Variance is the square of standard deviation

So answer should be

329.11/93 - (102.4/93)^2, same as lianmaster
charlize
27 Jun 09, 13:15

Die.

I am going to fail my maths soon.
SBS1984E
27 Jun 09, 13:38

Thanks! All. Erm Eagle, the "E" is representing what? The Sigma Sign?
eagle
27 Jun 09, 13:50

This one not related to your question... I just itchy hand post only

It means Expectation of X
Forbiddensinner
27 Jun 09, 13:54

Originally posted by SBS1984E:

Thanks! All. Erm Eagle, the "E" is representing what? The Sigma Sign?

E is the expected value. E(X) is the expected value of X.

The sigma sign means summation, which is the sum of all the values.
deepak.c
27 Jun 09, 14:26

Originally posted by charlize:

Die.

I am going to fail my maths soon.

There is still hope, get eagle to give you maths tuition.
Lee012lee
27 Jun 09, 21:50

Originally posted by SBS1984E:

Qn: 93 metal bars are manufactured by one machine. The length, x in metres, of each of the bars, is recorded.
The results are as follows: ∑x=102.4 and ∑x^2= â€Šâ€Š329.11

Based on the given question, how do I calculate the Variance and what does it mean?

The formula I have is

[ ∑ ( x_i - x*)^2] / n

x* = Mean of x. Dunno how to type it.

To simplify the variance formula first

                   ∑ ( x - x*)^2

Variance = ------------------- where x* is the mean of x

                          n

                  ∑ ( x^2 - 2xx* + x*^2)

Variance = ----------------------------

                             n

                  ∑ x^2 - 2x*∑ x + ∑ x*^2

Variance = -------------------------------

                                n

                 ∑ x^2            ∑ x         nx*^2

Variance = ------- - 2x*--------- + ---------

                   n                  n             n

                   ∑ x^2

  Variance = ------- -  x*^2

                     n

Varaince = [ ∑ x^2 ] /n - [ ∑ x /n ] ^ 2

Since ∑x=102.4 , ∑x^2= â€Šâ€Š329.11, n = 93

Variance = 329.11/93 - [102.4/93]^2 = 2.33
charlize
27 Jun 09, 22:09

Originally posted by deepak.c:

There is still hope, get eagle to give you maths tuition.

No money.

Poor students really are disadvantaged.

Haiz.
eagle
28 Jun 09, 00:08

Originally posted by charlize:

No money.

Poor students really are disadvantaged.

Haiz.

Not necessary.

Just need to work harder with the right mentality and the right methods.

I only found out many of my peers had tuition in JC recently... and I didn't have it

In a way, I was free to explore and "invent" many of my shortcut tips and tricks which I gladly teach to many people now, both on sgforums, sgclub and in tuition