The total wages for the 11 employees is:
$782*11 = $8602
Now add in the 12th employee's wages:
$8602 + $1261 = $9863
Now divide by 12:
$9863/12 = $821.92
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You can also do a weighted average:
New weekly average = (11/12)($782) + (1/12)($1291)
= $716.833 + $105.083 = $821.92