Can I call a cell value from inside a formula?

I am trying to process average values for something over more than a century with daily measurements converted to annual mean values. I am using the following formula to get annual averages for this value ...

=AVERAGEIFS(D:D,C:C,">=1/1/1903",C:C,"<=12/31/1903")

Here is my question. In this formula, instead of "1903" I would like it to call the cell value in the preceding column (in this case, column I; column config sample below question) so that I don't have to type in the year for 100+ formulas. Can I do that? And if so, ho?

Thanks for any help.

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COLUMN C ... COLUMN D ... COLUMN I ... COLUMN J (results)

Date ... Discharge ... Year ... Discharge, cubic feet per second (annual average)

... ... ... ... ... ... ... ... ... 1903 ... 465.64130435
10/1/1903 ... 910 ... 1904 ... 448.03278689
10/2/1903 ... 4580 ... 1905 ... 1697.29041096
10/3/1903 ... 5550 ... 1906 ... 1681.21917808
10/4/1903 ... 4170 ... 1907 ... 1079.21917808
10/5/1903 ... 3300 ... 1908 ... 3935.60928962
10/6/1903 ... 4400 ... 1909 ... 145.13150685
10/7/1903 ... 5750 ... 1910 ... 215.76164384
10/8/1903 ... 3300 ... 1911 ... 97.60000000
10/9/1903 ... 2200 ... 1912 ... 243.38251366
10/10/1903 ... 1370 ... 1913 ... 1072.18356164
10/11/1903 ... 1130 ... 1914 ... 1401.09863014
10/12/1903 ... 815 ... 1915 ... 2389.82739726
10/13/1903 ... 395 ... 1916 ... 1878.98633880

... continues until 2014

Here is a partial version of the sheet.

Thank you, Special-K. That seems to work great.