Check when iMac was woken from Sleep?

Hi all.
I'm a student, and on a limited broadband plan here in the UK. I thought it was going to be the start of a beautiful month now that my broadband had been reset back to 0gb in the past couple of days, but since the Mac update 10.8.4 my iMac data usage has sky rocketed!!

I updated OSX last night (off peak allowance) and yesterday my computer downloaded 20Gb in the day! I checked my history a couple of youtube videos, but nothing that would make it climb so high!

I emailed them and they showed me when the most was being downloaded. Is there a way to check to see what times the iMac was woken from sleep as you can do with startup? this would be useful in seeing if the times correlate.

tldr: can I check to see what times the Mac was woken from sleep? Is there anyway to check what data my mac was downloading? Thanks

 

Thanks, not sure what to be looking out for exactly. It appears to be mostly outdated anti-malware software 'talking' in there.

Code:

ClamAV update process started at Thu Jun  6 16:45:09 2013
DON'T PANIC! Read http://www.clamav.net/support/faq
main.cld is up to date (version: 54, sigs: 1044387, f-level: 60, builder: sven)
Downloading daily-17302.cdiff [100%]
Downloading daily-17303.cdiff [100%]
Downloading daily-17304.cdiff [100%]
Downloading daily-17305.cdiff [100%]
Downloading daily-17306.cdiff [100%]
Downloading daily-17307.cdiff [100%]
Downloading daily-17308.cdiff [100%]
[LibClamAV] ***********************************************************
[LibClamAV] ***  This version of the ClamAV engine is outdated.     ***
[LibClamAV] *** DON'T PANIC! Read http://www.clamav.net/support/faq ***
[LibClamAV] ***********************************************************
daily.cld updated (version: 17308, sigs: 1302505, f-level: 63, builder: ccordes)
DON'T PANIC! Read http://www.clamav.net/support/faq
bytecode.cld is up to date (version: 214, sigs: 41, f-level: 63, builder: neo)
[LibClamAV] ***********************************************************
[LibClamAV] ***  This version of the ClamAV engine is outdated.     ***
[LibClamAV] *** DON'T PANIC! Read http://www.clamav.net/support/faq ***
[LibClamAV] ***********************************************************
[LibClamAV] ***********************************************************
[LibClamAV] ***  This version of the ClamAV engine is outdated.     ***
[LibClamAV] *** DON'T PANIC! Read http://www.clamav.net/support/faq ***
[LibClamAV] ***********************************************************
Database updated (2346933 signatures) from database.clamav.net (IP: 217.135.32.99)

That's all I can really see in here. Anything else I can do that might help?

 

Thanks all, that was much help, especially telling me which log to look in! The data mystery continues