number of days with measurements in each 7 day period

There are 3 formulae in the sheet. Different shading = different formula. The one that does the heavy lifting is this:

=IFERROR(1/(1/SUM(IF(FREQUENCY(IF(($A$2:$A$700=F$2)*($C$2:$C$700="x")*($B$2:$B$700<>"")*($B$2:$B$700>=F$3+7*(ROWS(F$4:F4)-1))*($B$2:$B$700<F$3+7+7*(ROWS(F$4:F4)-1)),$B$2:$B$700),$B$2:$B$700),1))),"")


See sheet.

IMPORTANT>>>>
You seem to be using an older version of Excel than me. So, please refer to the attached file. If the formulae are enclosed within a pair of { }, these are array formulae.

These are a little different from ordinary formulae in that they MUST be confirmed in the FIRST CELL ONLY by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER. After that, the array can be dragged down as normal, to cover the desired range.

You will know the array is active when you see the curly brackets { } appear around the outside of your formula. If you do not use CTRL+SHIFT+ENTER you will (almost always) get an error message or an incorrect answer. Press F2 on that cell and try again.

Don't type the curly brackets yourself - it won't work...