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Calculating Quarterly Averages From Daily Data

I have a sheet with daily data starting from 01/01/2000. I want to calculate daily averages for each quarter (i.e 2000Q1 value will be the average of values between 01/01/2000-31/03/2000, 2000Q2 will be average of values between 01/04/2000-31/06/2000, 2000Q3 average(01/07/2000-31/09/2000) and 2000Q4 will be the average of (01/10/2000-31/12/2000) etc. for all years afterwards.

I want to have the values in the corresponding cells starting with range ("e2")

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