Yes and no. Google purchased Applied Semantics back in 2003. Initially they needed the technology for their AdSense program to search through content to find a pattern of words so their robots could work out what the theme of the page content was. Once the robot had worked out the page theme, the AdSense ads were served to be relevant to that page theme. I'm sure you have all noticed how good AdSense ads are at serving up ads that match the theme of a web page. Google soon started using the technology to work out what each web page in general was about so it could determine where the page should rank in the index. The Google robots look for patterns of words that follow a theme so they can determine what the page is about, and also determine how well that page is themed, and therefore how well it provides information on that theme. The Google robots DO NOT look for keyword density! Read that again please... The Google robots DO NOT look for keyword density! However, when a main keyword is repeated a number of times throughout a web page, as it must naturally be, then Google gets a better idea of the theme of the page. When the keyword is repeated too many times it no longer reinforces the theme, but rather becomes a false and stilted piece of "content." Google's robots can recognize this too and the ranking of the page will reflect how Google feels about the value of keyword stuffing. When not only the main keyword, but also synonyms of the main keyword, alternative meaning of the main keyword and relevant terms related to the main keyword are included in the page, Google's robots have no difficulty knowing what the theme of the page is. Additionally, as the page is now rich in the kind of words that Google's Applied Semantics technology likes to see, the page will be ranked much higher, and will be much more stable and stronger that it would ever be with just a single keyword added to a certain density. Keyword density does not have a role with Google. Latent semantic indexing does. Writing an article with a keyword density of say, 3% means that you are, as far as Google is concerned, using theme words to indicate what the theme of the page is about. However, you are not using very many theme words, so the page will need lots of backlinks to help it rank well. When you theme a page properly, you hardly need backlinks! Read that again... When you theme a page properly, you hardly need backlinks! Your article will outrank nearly everything as it will be much closer to Google's ideal page rich in descriptive theme words, than one where a single keyword is repeated a number of times in a pathetic attempt to convey the complexity of the page theme. It's not just me saying this - Google is saying it too, and of course, Google said it first. Google is saying loud and clear what it wants, and sadly, it seems no one is listening. What do you think the recent Panda update was all about? It was Google saying it wants properly themed content in its index that conveys the very best kind of information to the readers. This is really so simple. Why complicate it with the antiquated concept of keyword density? John.
I think standard keyword density should be somewhere in between 1 to 1.5% for the main keyword and it should sound natural not "Inserted". In order to keep the article SEO friendly you should find out some relevant key phrases that imporve the flow of content not work like an obstacle. Hence you can achieve the standard keyword density of 2 to 3% without being too spammy and get banned.
jcoutts1 has provided as clear of an explanation for how the search engines work as I have seen. Sometimes, we have too much obsession with a specific keyword density instead of addressing the "theme" of the article by using Latent Semantic Indexing. Personally, I always write my articles now by starting with a primary keyword and then adding Google's own Related Searches results at the bottom of the page and exploring other keywords using the Google Wonder Wheel. Google gives you the answers to the quiz; all we have to do is follow it.