Is there a way to upgrade the Splunk version through Splunk UI (Splunk Web)? ...i.e from the search head as we upgrade and install the apps..
No, you have to do it using the instructions on the splunk website, e.g., untarring the files over the existing directory.
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I AM NOT suggesting that you should do this, only that you could do it and that you might be able to make it work:
More details here: http://docs.splunk.com/Documentation/Splunk/latest/Installation/HowtoupgradeSplunk