Right Keyword Density for Search Engine Optimization

We all know that for top ranking on any search engine, unique content and appropriate keyword rich content is the major factor. Now how rich and how frequently should a key word appear is the moot question. What is primary keyword for the article and how often should it be used? Does a search engine read like human; from top to bottom and from left to right and if so should keywords be populated at beginning of the article or at the bottom?
Before these questions, some understanding of "Keyword Density".
In simple words keyword density is number of times a particular word appears in your article per hundred words. Say if a particular word appears 110 times in an article of 1000 words, they keyword density would be 11%. There are many sites that can give you automatically the keyword density of your page such as www.live-keyword-analysis.com

Unfortunately, keywords analysis is not so simple. The way search engine would see it is as complex measure of keyword density taking into account the text components in the page such as the Meta tags, Title, Keywords, Alt Text, Description, and Comments. When using this measure, you don't just count the words your visitor sees; you also count the words in your Meta tags. In the above example, if you have 110 words on your home page, 10 words in your Title tag, 20 words in your Description tag, 70 words in your Alt tags, and 10 words in your Comments tag, your total word count for the page is 110 + 10 + 20 + 70 + 10 = 220.
Similarly, when counting keywords, you don't just add up the number of times a visitor will see your keyword, you also count the number of times that keyword appears in your meta tags. For example, if your keyword appears 5 times in the home page copy, 3 times in the Title tag, 5 times in the Description tag, 30 times in your Alt tags, and twice in your Comments tag, your total keyword count is 5 + 3 + 5 + 30 + 2 = 45. So with a total word count of 210 and a keyword count of 45, your keyword density is 45/210 x 100 = 21%. It is argued that this measure of keyword density is more relevant as the search engines measure density in this fashion. For finding the keyword density of your page using this more complex measure, please visit GoRank.com
You need to be very aware of which measure you're talking about when you're talking "keyword density". Mostly when people talk about keyword density, they're talking the simple measure.
What should be Optimum Keyword Density, so that it is not overdone?
And now down to business... What keyword density (of either kind) should you be targeting on your website? There's a lot of debate surrounding this issue because the search engine companies don't disclose the details of their algorithms to avoid people to abuse the system. Instead, people working in the SEO world are left to figure it out based on their experience.
Reputed SEO experts, feel that Google sees pages with a keyword density of greater than 2% as spam. It was this article which prompted me to analyze the keyword density of my copywriting website. For one article that was tested, the average keyword density of the article is 1.9%, while using the complex measure it's 4.9%.
Keyword Density Range: Using the simple measure, the density ranged from 0.4% to 7.6%. Using the complex measure it ranged from 1.6% to 17.5%
The figures and corresponding ranking detailed in this case study may not be directly relevant to every site. There's a lot I don't know about the algorithms and there are bound to be other factors at play which I don't know about.
The range figures are noteworthy because they suggest that you don't need to be paranoid about having some pages with a very high density and some with a very low density. A simple keyword density of 1.9% can be enough for a first page ranking in Google.com, of course, assuming you have enough quality back links.