Using the sample data you posted (and adapting it slightly), here is my attempt to solve the problem:
SELECT BASESCORE,
Datediff(dd, MINDATE, MAXDATE)
FROM (SELECT BASESCORE,
Cast(Max(DATETIME) AS DATETIME) MaxDate,
Cast(Min(DATETIME) AS DATETIME) MinDate
FROM table1
GROUP BY BASESCORE)T
You can take a look at the full working version on SQL Fiddle.
Let me know if there was something I misunderstood 😉