Which statistics option allows statistics to be updated while a query executes against the object the statistics are based on?

The correct choice is the option that refers to "Auto Update Statistics Asynchronously." This option allows statistics to be updated while a query is executing against the database object, ensuring that the query can continue running without waiting for the statistical information to be updated. This is particularly beneficial for long-running queries or those executed against large datasets since it can enhance performance and maintain timely execution.

When the auto-update statistics feature is set to asynchronous, the SQL Server engine can allow queries to use existing statistics during execution, while simultaneously updating the statistics in the background. This minimizes delays and helps in maintaining optimal query plans without significant performance loss.

The other options do not provide this kind of real-time updating capability during query execution. Manual update statistics requires explicit commands to be executed to refresh the statistics, while standard auto-update statistics will block query execution until the statistics are updated, which can lead to performance bottlenecks. Additionally, the option referring to update statistics on query completion implies that updates will only occur after the query has finished executing, thereby potentially introducing latency into the process.