The sentence comes from here:
''The best thing about being a statistician,'' Mr. Tukey once told a colleague, ''is that you get to play in everyone's backyard.''
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A backyard is a private part of your property that is not central, but closely connected to where you live.
Metaphorically, it must be a part that is with the boundary, but towards the edge, but "behind the scenes" or private in some way.
One possible interpretation of this (in context) is that the statistician works in the "academic backyard" of the economist, physicist, biologist, etc. A statistician will use and develop techniques of use in other specialities, while not being a member of any of those specialities.
So, for example, a statistician who is analysing population data of an animal is "playing in the biologist's backyard". They are working with biological data, and are close to the biologists' metaphorical "home". This is "the best thing", because, as a statistician, you learn lots of stuff about economics, physics, biology. The statistician is not tied to any single specialism and their work doesn't become boring.
Mr Tukey, who said this, worked with data on human sexuality, environmental science and computer engineering. In the article, this quote is used to illustrate the wide number of fields that Mr Tukey had worked in.