Partition of a table - how to minimize the time offline? How to check if all the statistics were updated?
from the technical article Statistics Used by the Query Optimizer in Microsoft SQL Server 2008statistics are out of date when:


  
  The table size has gone from 0 to >0 rows.
  The number of rows in the table when the statistics were gathered      was 500 or less, and the colmodctr of the leading column of the
  statistics object has changed by more than 500 since then.
  The table had more than 500 rows when the statistics were gathered,    and the colmodctr of the leading column of the statistics object has
  changed by more than 500 + 20% of the number of rows in the table
  when the statistics were gathered.
  


Moreover you can use dmv sys.dm_db_stats_properties to check when stats were last updated

SELECT
OBJECT_NAME([sp].[object_id]) AS "Table",
[sp].[stats_id] AS "Statistic ID",
[s].[name] AS "Statistic",
[sp].[last_updated] AS "Last Updated",
[sp].[rows],
[sp].[rows_sampled],
[sp].[unfiltered_rows],
[sp].[modification_counter] AS "Modifications"
FROM [sys].[stats] AS [s]
OUTER APPLY sys.dm_db_stats_properties ([s].[object_id],[s].[stats_id]) AS [sp]
WHERE [s].[object_id] = OBJECT_ID(N'table_name_here');


Also suggest you to go through article Understanding When Statistics Will Automatically Update