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This result means that the average is `midway' between the numbers in an interesting way. Imagine you are sitting at the average, with the smaller numbers to your left and the larger numbers to your right (recall that the smaller numbers have negative distance, and the larger ones have positive distance).
The facts
- Distance from average to smaller numbers is negative
- Distance to larger numbers is positive
- Total distance (from average to larger and smaller numbers) is 0
Conclusion: The sum of distances from the smaller numbers = sum of distance to larger numbers. If they were unequal, the total distance would not be zero. Since the total distance is zero, then they must be equal. Another way of putting it: if you have a bunch of good and bad effects, and the net result is zero, then the sum of the good effects = sum of bad effects.
(If that isn't satisfying (and I hope it is!), here is a math explanation.
2)
Fact to take away: sum of distance above average = sum of distance below average
Next: Consequences
Up: Mathematical Properties of the
Previous: Distance to the average
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Kalid M. Azad
2002-10-31