I've got a lab assignment to compile linux kernel , so I wanted to ask if its safe to install latest kernel (3.19.3) on my current Ubuntu 14.04 , I've got important data on my laptop so I cant afford to experiment
I wouldn't recommend it. Not only would you have to reboot the same machine you're developing with (interrupting your work flow), but you might accidentally build a kernel that is missing some hardware drivers your laptop uses.
If you do that, you can hold down Shift during boot to get the grub menu and boot an official kernel instead of your custom one. So you won't ruin anything.
But I'd recommend instead using a virtual machine like VirtualBox or kvm to boot your kernel inside a safe fake machine.
You can always afford to experiment provided you begin with a good disaster recovery plan. muru suggestion (in comments) to use a virtual machine is likely the safest and perhaps easiest solution (to take that approach see this and this ).
However, provided you have current backups ( see this and this ) and a known good live media of your current system it's highly unlikely that you will lose anything other than a little time (even in the event of an epic failure)
If something kernel related goes wrong, you can always choose to boot your system with your previous version of the kernel from the Advanced Options in the GRUB menu.
I've found experimentation to be one of the best ways to obtain experience and I recommend it whole-heartedly.