Choose the most appropriate option. The mean of $72$ items was found to be $63$. If two of the items were misrecorded as $27$ and $9$ instead of $72$ and $90$ respectively, find the correct mean.

The original sum of the 72 items is 72 times 63, which equals 4536. To find the correct sum, we subtract the misrecorded values 27 and 9, and add the correct values 72 and 90, yielding a new sum of 4536 - 36 + 162 = 4662. Dividing this correct sum by 72 gives a correct mean of 64.75.

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