What’s the weather like? It’s the classic New England question as well as a Boston Marathon staple. But for all the seemingly exact details on heat and headwinds, and for all that the annals of the Boston Marathon are saturated with weather stories, the answer has historically lacked precision. That will change Monday, when students from the state’s only undergraduate meteorology program, at UMass Lowell, will be stationed at key points from Hopkinton to Boston to take readings on temperature, humidity, wind speed, and wind direction and relay them in real time to the marathon media center.