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1

As it was already pointed out in other answers, you have to select at least two cells containing successive dates. However, this didn't work for me at first because my Google Sheet had the wrong locale and the cells had the wrong formatting. Set the locale for your Google Sheet: File menu → Spreadsheet settings... → Set the correct locale Configure ...


2

To find the number that's halfway between A2 and B2, use the formula =(A2+B2)/2 (You'll need to apply a suitable date format to the output.)


1

You can use =datevalue("01-"&B2) (single-cell formula that can be copied down), or =arrayformula(datevalue("01-"&B2:B)) (converts an entire column at once), or =arrayformula(iferror(datevalue("01-"&B2:B))) (does the same, while suppressing any error messages). This works because the strings like 01-Oct-14 are understood by datevalue ...



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