Gemstones Rarest vs. Most Expensive - Top Ten Gems?

I thought it would be interesting to find out what the most rare gemstones are.  When searching I found lots of varying opinions, which I assume were due to the posts being different years and newer discoveries or older mines playing out.  Some considered one-location gemstones rare even though the site may produce tons of stones.  There were also differing opinions on which were the ten most expensive, some of the confusion being caused by sites counting down 10 to 1 or up 1 to 10.  Values were based on what the store sites were selling stones for or the current appraised value - so always search for current year pricing.  Diamonds showed up most lists, although they are not RARE, they are usually the most expensive because they are the hardest gemstone and are very refractive.  I tried to find an infographic I could use, but the ones I liked were copyrighted.

Many of the sites were just copies of others, of the sites that were different the 10 most repeated gemstones (in no particular order) are:
- Diamond (although different colors were featured) 
- Alexandrite
- Black Opal
- Bixbite (red beryl)
- Tanzanite
- Jadeite
- Taaffeite
- Benitoite
- Musgravite
- Painte

Under expensive also included were Emerald (green beryl),  Ruby, and Sapphire. Under rare included were Poudretteite and Grandederite.

Below is a list of the best links I found that contain either great photos of the gems or,\ the most detailed information.
  10 Most Valuable Gemstones in the World photos from Pearl Source 2018
  Top 10 Investment Gems photos from AJS Gems 2018
  10 of the World’s Rarest Gemstones photos from Mental Floss 2016
  The World’s Top 10 Rarest and Most Expensive Gemstones photos from True Facet 2015

  Top 10 World’s Rarest Gems infographic from SEO Surfer 2015
  The Most Expensive Gemstones in the World infographic from Gem Coach 2013