Final answer:
Statement C is not true because the difference between mean solar time and apparent solar time can be up to about 14 to 16 minutes, not just 4 minutes.
Step-by-step explanation:
The statement about mean solar time and apparent solar time that is not true is: C) Mean solar time and apparent solar time are always within about 4 minutes of each other. This statement is incorrect because the difference between mean solar time and apparent solar time, also known as the equation of time, can be as much as about 14 to 16 minutes. The other statements are true: Apparent solar time does indeed measure noon when the Sun is on the meridian (A), mean solar time sometimes runs ahead of and sometimes behind apparent solar time due to the equation of time (B), and mean solar time is based on the average length of the solar day across an entire year (D).