For WITH SAMPLE 50 PERCENT
it works as though for each data page in the table SQL Server flips a coin. If it lands heads then it reads all the rows on the page. If it lands tails then it reads none.
Tracing the UPDATE STATISTICS T WITH SAMPLE 50 PERCENT
call in Profiler shows the following query is emitted
SELECT StatMan([SC0], [SB0000])
FROM (SELECT TOP 100 PERCENT [SC0],
step_direction([SC0]) OVER (ORDER BY NULL) AS [SB0000]
FROM (SELECT [C] AS [SC0]
FROM [dbo].[T] TABLESAMPLE SYSTEM (5.000000e+001 PERCENT)
WITH (READUNCOMMITTED)) AS _MS_UPDSTATS_TBL_HELPER
ORDER BY [SC0],
[SB0000]) AS _MS_UPDSTATS_TBL
OPTION (MAXDOP 1)
With Plan
TABLESAMPLE SYSTEM (5.000000e+001 PERCENT)
is responsible for the sampling and is documented hereis documented here
TABLESAMPLE SYSTEM
returns an approximate percentage of rows and generates a random value for each physical 8-KB page in the table. Based on the random value for a page and the percentage specified in the query, a page is either included in the sample or excluded. Each page that is included returns all rows in the sample result set.
The documentation also states
Although the plan shows a table scan is performed, only those pages that are included in the result set are actually required to be read from the data file.
The STATMAN
call is to an internal aggregate function briefly described here