What is Variance?

SBS1984E SG

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= 329.11

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 SG

I think u need to expand the formula above and then sub in the values.

charlize SG

You can start by calculating the mean which is 102.4 / 93

SBS1984E SG

But how do I get the values from ∑x=102.4 and ∑x^2= 329.11 only? The mean I calculated as 1.10m, then how do I proceed?

charlize SG

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= 329.11 and somehow try to sub it into the equation together with the mean u found.

charlize SG

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 SG

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 SG

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 SG

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 SG

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 SG

Also standard deviation formula from wiki is

So answer should be

329.11/93 - (102.4/93)^2, same as lianmaster

charlize SG

Die.

I am going to fail my maths soon.

SBS1984E SG

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

eagle SG

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

It means Expectation of X

Forbiddensinner SG

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 SG

Die.

I am going to fail my maths soon.

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

Lee012lee SG

To simplify the variance formula first

∑ ( x - x*)^2

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

∑ ( x^2 - 2xx* + x*^2)

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

∑ x^2 - 2x*∑ x + ∑ x*^2

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

∑ x^2 ∑ x nx*^2

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

n n n

∑ x^2

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

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

Since ∑x=102.4 , ∑x^2= 329.11, n = 93

Variance = 329.11/93 - [102.4/93]^2 = 2.33

charlize SG

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

No money.

Poor students really are disadvantaged.

Haiz.

eagle SG

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