It is a common figure of speech to refer to people in their late 40s or 50s as middle-aged; common enough to be ingrained in concepts like "middle-age crisis". It is technically correct, since this age represents the midpoint of one's adult life with modern life expectancy.
In most modern nations, "adult" refers to someone over 18 to 21. With life expectancy of over 70 years, that places middle age exactly in the middle of 50-year period. I thought that was obvious enough.
