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I'm making a form where people can enter in certain dimensional grades for a specific name. So each row of the spreadsheet will probably read something like:

Name | Strength | Agility | Luck 
John |     8    |     7   |   1

...etc. But John and his peers may be graded many times, so their names will continue to appear down the spreadsheet. I'd like a way to take specific peoples' grades and enter the averages of their dimensions somewhere else in the spreadsheet (or a different spreadsheet). Is there a way for me to do that?

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Use AVERAGEIF :

=AVERAGEIF(B4:B6,B10,C4:C6)

B4:B6 - column Name C4:C6 - column Strength (for exmpl.) B10 - specific name

This function is available only in New Google SpreadSheet: https://support.google.com/drive/answer/3256529

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Because a Form it may not be advisable to have the condition name in the same column as the range of names (OP has mentioned their names will continue to appear down the spreadsheet). This could also be a problem where the ranges are predetermined (eg B4:B6).

However, applying the same function as @jacek2V I would suggest something more like:

 =averageif($B:$B,$I2,C:C)  

in part because also easy to extend to more than a single attribute (ie copied across and down to suit):

WA54647 example

The above requires that ColumnI in the example is populated with one instance of each name in ColumnB in the example, which might be achieved with:

=unique(B:B)  

in I1.

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An alternative to current (unaccepted) offers is a pivot table:

WA54647 example

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