Yes, there is actually a very easy way. When you take the mean of a set of numbers, the "residuals" will add to zero.
For example: the average of 7, 8, 9, 10, 11 is 9, and:
7 - 9 = -2
8 - 9 = -1
9 - 9 = 0
10 - 9 = 1
11 - 9 = 2
(-2) + (-1) + 0 + 1 + 2 = 0
This property allows you to start with a "base" number and calculate the residuals from that number to determine where the mean is.
From your example, we can find the average by taking a base number, say 1000, and calculating the sum of the residuals:
993 - 1000 = -7
994 - 1000 = -6
996 - 1000 = -4
997 - 1000 = -3
998 - 1000 = -2
1001 - 1000 = 1
1001 - 1000 = 1
1002 - 1000 = 2
1004 - 1000 = 4
1004 - 1000 = 4
The sum of these numbers is (-7) + (-6) + (-4) + (-3) + (-2) + 1 + 1 + 2 + 4 + 4 = -10
1000 is thus not the mean, but you know that the mean -10/10 lower than 1,000 (since there are 10 numbers that make up the average). The average is 1000 - 1 = 999. This is MUCH easier than trying to sum the numbers and divide.
Another quick example. The average of 650, 662, 668, and 676. Let's take 660 as a base:
650 - 660 = -10
662 - 660 = 2
668 - 660 = 8
676 - 660 = 16
Sum of residuals: 16
Number of observations: 4
+16/4 = 4
The average is thus 660 + 4 = 664.
