Proper Keyword Density Range for each search engine?

As we know,when the Keyword Density is too low,search engines may think lowly of the Keyword.
When the Keyword Density is too high,serach engines may penalize the corresponding website.
And different serach engines have different analysis algorithms for the Keyword Density.
Then,here comes the question--What is the proper Keyword Density Range for each search engine?

For Google it is 0.2% to 4% . 4% is an average keyword density but it varies according to the kind of site and niche.

2% to 4% is used normally and it is ideal from every aspect.

2%-4% is the ideal density. But what is the normal keyword density? I mean is there a minimum or maximum dense for keywords?

Hi, Keyword density for a web page has greater priorities in Google so try to write content measuring keyword density 4 to 5%.

Nowadays, keyword density is less important... It is acceptable as long as it is organically placed in the text.
You can exceed the limit if required, of course overdoing of everything is bad.
So place keywords wherever they are required.

You have to find a happy place in between the two. Try your keyword once every other paragraph or twice every three hundred words. I guess that's equal to 1.5%. Most people I write articles for will ask for a density of 2-4 percent, maybe I'm a little jaded when it comes to my own content now.

I thinks it's not about the density, there is no ideal value. ? On the other hand, words used more often then other words on a page are likely to be the more important terms.. and they naturally have a higher keyword density.
I prefer to check WHERE the keywords occur..in the Title, in Headings, in URLs etc. Some keyword Density tools show both. Try the Keyword Density Analyzer at ranks.nl?  for example (free tool)

3-4% is average keyword density applicable for all search engines..