This could be achieved by adding a formula field in the Table view (or upstream, in the DataManager), creating the dynamic line that will always be up-to-date, something like
SUBSET_MEAN([Value], SUBSET([Period])

If you were to use the same formula inside the Bar/line view, as a measure function, the value would be correct only if you have histogram-type split e.g. Jan-Mar, Apr-June etc.
as every period will have a different mean, however this will not create a flat line across the chart, while the first option will. Under the Measures menu you should choose the Mean function for this field.

Hi Paula

The first idea won work because i want the mean value to update if the user select a wider or narrow date range on the RHS filters on the tab, or indeed if they filter by any other metric on the RHS

Also i want the average flat across the graph independant of the split.For instance split share price by date i would want the average over the date range rather then the average per day

You will need to introduce 2 variables, for start/end dates and use them in the formula field.

SUBSET_MEAN([Value],
SUBSET2([Date],[Date],[Start date],[End date],">","<"))

Demo file attached.