Your question here is accuracy, but I think you are missing the bigger picture on rankings. Google does so much personalization on search results, there is no single "rank" for a given page on a given key term. If you are signed in, Google will rank pages higher that you visit a lot. Even if you are not, Google may rank pages higher that relate to your geographic location. Whenever a tool is pulling a KW ranking, it is doing so with a set of parameters that may be different than another tool and so the results may vary. Some people have even called them useless http://www.wordstream.com/blog/ws/2014/08/11/seo-rank-checking
Dr. Pete did an article on this recently to compare different methods of measuring rank
https://moz.com/blog/comparing-ranktracking-methods-browser-vs-crawler-vs-webmaster-tools
While he found differences, they were not that huge across tools.
Your best advice is to find a tool that will report what you need and stick with it. Consistency is the key. That way you can at least know that if there is a change that the change did occur and in what direction. You want a baseline and then to know once you make a change are you doing better or worse. You will find discrepancies if you were to compare Moz, Keyword Planner, Google Webmaster Tools, CognitiveSEO, Authority Labs, etc etc. Everyone measures it slightly differently and you see some differences due to Googles personalization. Heck, take a read of the Search Console Help Google calls is an "average position" due to personalization of results when they show ranking results https://support.google.com/webmasters/answer/35252?hl=en
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Average position: The average top position of your site on the search results page for that query. With change also shows the change compared to the previous period. Green indicates that your site's average top position is improving.
To calculate average position, we take into account the top ranking URL from your site for a particular query. For example, if Jane’s query returns your site as the #1 and #2 result, and David’s query returns your site in positions #2 and #7, your average top position would be 1.5.
I know this does not answer the question you asked, but I hope it gives you the question you need to understand to put all this in perspective. Get a reputable Keyword tool that gives you the data output that you need for reporting. Stick with it and you will do fine.
Cheers!