How can I refer to the year 1950 in terms of centuries?
At/in the middle of 20th century, there were great improvements in the transport system.
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You can be "at a point", or "in a region". Thus, you can be "at the midpoint" of something, or "in the middle" of something. You can also be "at an hour" or "on a day".
The following options sound natural to my (American) ear:
The following options are grammatically correct. They are awkward, because they force the reader to do a lot of math:
The following option does not sound natural, but was used as the title of a funny short film: