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The phrase "estimated number of" is correct and usable in written English.
You can use this phrase when you want to express an educated guess of the quantity of something. For example, "The estimated number of people who attended the concert was 5,000."
Exact(60)
The agency published the estimated number of people receiving antiretroviral treatment by country for 49 countries.
The size of each "region" reflects the estimated number of user accounts.
M ^ : estimated number of migrants between two populations.
Estimated number of pages: 2 pages or less," or whatever.
Estimated number of malaria deaths by WHO region, 2000 2015.
Figure 1: Estimated number of known living species.
Estimated number of devices running different versions of Android to Oct 2012.
Estimated number of beneficiaries: 4 million.
Estimated number of fighters is 3,000 to 5,000.
Fig. 3 Estimated number of targets against ground truth.
2.5 million: Estimated number of spectators along the course for this year's race.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com