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Are there any statistics regarding how many units each manufacturer has sold, e.g. in 2019?

An article from 2016 claims Monoprice to have led the market back then - but all of the printers in that article have become obsolete since then. Some manufacturers also claim theirs to be "one of the most popular" - but that likely doesn't translate to sales, at least for the more overpriced ones.

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Getting this data is not easy. Many companies that make 3D printers are either private companies that do not report results or are larger companies where 3D printers are one of many products they manufacture. Some companies study this information through mining public sources and surveying users for their opinions and experience. The result of some of these studies are available for a fee.

Occasionally, a trade publication will survey data sources and produce an article. In other cases, a trade pub will publish an article generously offered by a commercial contributor.

It is always difficult to know what is true when abstracting information from obscured, noisy, and biased information sources.

Your question itself includes a bias. You use a words that include a value judgement: "but that likely doesn't translate to sales, at least for the more overpriced ones."

The article you reference is not a deeply researched investigative piece. It is simply some product details for the five printers in 2016 which sold the most on Amazon.com. It doesn't include printers which were not sold on Amazon, so it leaves out any printers which use a different distribution channel. Also, the article include an link, probably which generate revenue back to the magazine, to each of the five printers sold through Amazon.

To summarize, it is very difficult to aggregate this kind of information. Those who try to do so like to be compensated. A list of the top five devices on Amazon is a biased list.

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    $\begingroup$ And regarding alternate distribution channels: for some products, Amazon might be representative of the overall market. But 3d printers sell of LOT of their units into education and light manufacturing, both of which tend to use channels other than Amazon. I wouldn't expect Amazon to be at all representative for this item. $\endgroup$ – Joel Coehoorn Jan 13 at 17:38
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For sales figures of the smaller companies; it is very difficult because they don't publish (esp the Chinese brands). For the larger organizations there is

The Wholler's Report https://wohlersassociates.com/2019report.htm

An article on Forbes gave a quote about the 2018 Wholers Report:

The 2018 report has the estimated number of desktop systems sold at nearly double the 2015 data (reported in the 2016 report). In just over two years, an astonishing 528,952 desktop 3D printers (or systems) are believed to have been sold.

For 24 Years (basically the start) they have been tracking the 3D printing industry, providing the most reliable source of market share and growth. It costs a bit to purchase and you can't share the contents with anyone else, but if you're really interested then; grab a copy.

Further, there are the statistics of 3DHubs.com. They used to be a distributed 3d printing service (I guess they still are). They keep track of the most popular printers of all types:

https://www.3dhubs.com/get/trends/

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