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Actually not easy with a standard filter - when you apply a filter it only keps the value selected, all other data is removed. Therefore if you select July 2015 only that month is kept.
You are able to use parameters to do this. Create a parameter with your month/year values and then create a calculated field to use that parameter. The mechanics of the calculated field depend very much on how you set up the parameter but it'll be something like [DateField]<=[Parameter].
The downsides of parameters are the values don't update as more recent data becomes available - i.e. when it becomes October 2016 the value October 2016 won't automatically appear in the parameter.
If you're not familiar with parameters I suggest you quickly read up on them, there are a lot of articles about them and posts in the community, for example this similar question from very recently: Graphs .