Sum of squares for variance Help!

• October 12th 2008, 08:15 AM
nugiboy
Sum of squares for variance Help!
Heres the question:

Quote:

The Royal Automobile Association defines peak-time as 6 am to 6 pm, Monday to Friday. It records the number of vehicle breakdowns reported per hour. The figures for a random sample of 40 peak-time hours in a certain area are as follows.

http://i137.photobucket.com/albums/q...iger/Stats.jpg

i. Find the mean and variance of the data.

I worked out the mean to be 0.5, which is right, but im stuck on the variance part.

I know the formula for variance to be $s^2=\frac{S_{xx}}{n-1}$

So i need to find $S_{xx}$, which is $S_{xx}=\sum{x^2}-n\overline{x}^2$

Im a bit stuck on the $S_{xx}$ part due to one of the x values being '4 or more'. Normally i wouldn't have a problem with these sorts of questions, but they usually just have single values for x.

How would i use '4 or more' in the formula. Should i just do $0^2+1^2+2^2+3^2+4^2$... etc, or is there something else i need to do?

Any hints?

• October 12th 2008, 08:54 AM
CaptainBlack
Quote:

Originally Posted by nugiboy
Heres the question:

I worked out the mean to be 0.5, which is right, but im stuck on the variance part.

I know the formula for variance to be $s^2=\frac{S_{xx}}{n-1}$

So i need to find $S_{xx}$, which is $S_{xx}=\sum{x^2}-n\overline{x}^2$

Im a bit stuck on the $S_{xx}$ part due to one of the x values being '4 or more'. Normally i wouldn't have a problem with these sorts of questions, but they usually just have single values for x.

How would i use '4 or more' in the formula. Should i just do $0^2+1^2+2^2+3^2+4^2$... etc, or is there something else i need to do?

Any hints?

You can ignore the 4 or more because its frequency count is 0.

and you should have:

$
S_{xx}=\left(\sum{f_i x_i^2}\right)-n\overline{x}^2
$

and for that matter:

$
\bar{x}=\frac{1}{n}\sum{f_i x_i}
$

CB
• October 12th 2008, 09:05 AM
nugiboy
Quote:

Originally Posted by CaptainBlack
You can ignore the 4 or more because its frequency count is 0.

and you should have:

$
S_{xx}=\left(\sum{f_i x_i^2}\right)-n\overline{x}^2
$

and for that matter:

$
\bar{x}=\frac{1}{n}\sum{f_i x_i}
$

CB

ok il try the other formula it looks a it easier.