But, before I get to why - let me clarify what the option does.
I've heard a few folks say that it stops SQL Server from updating the statistics at the time of a rebuild; that is NOT what it does.
NOTE: STATISTICS_RECOMPUTE only works when creating or rebuilding an index.
If you want to stop the auto-updating of a column-level statistic you use NORECOMPUTE when creating that particular statistic.
Evenly distributed data tends to be easier to represent in a histogram (one of the pieces of information maintained in a statistic in SQL Server).
However, might be much more uneven (and therefore skewed).
The more difficult question is if/when this would make sense to turn off – for either an index or a column-level statistic.
And, yes, there are some cases where this can be appropriate.
Related: Making the Most of Automatic Statistics Updating The case where it makes sense to be turned off is for tables that are large in size and have very skewed data distribution.
For example, the ratio of might be very evenly distributed between 1 and 3 items with an average of 2.1.