Answer:
Where the sum of the distances to the right of the mean equals the sum of the distances to the left of the mean.
Step-by-step explanation:
The mean can be thought of as the balancing point of a distribution, to understand this phrase see this distribution that consists of 14 samples:
1 4 5 6 10 11 13 19 22
1 5 13
1
1
The mean of this distribution is (1+1+1+1+4+5+5+6+10+11+13+13+19+22)/14 = 8
1 4 5 6 P 10 11 13 19 22
1 5 13
1
1
P represents the mean,8, of the distribution but it is also the balancing point, to see this calculate the distance between the mean and each point:
Distance between P and 1: 8-1 = 7
Distance between P and 4: 8-4 = 4
Distance between P and 5: 8-5 = 3
Distance between P and 6: 8-6 = 2
Distance between P and 10: 10-8 = 2
Distance between P and 11: 11-8 = 3
Distance between P and 13: 13-8 = 5
Distance between P and 19: 19-8 = 11
Distance between P and 22: 22-8 = 14
The sum of the distances between the mean and every point in the left is = 7+7+7+7+4+3+3+2 = 40
The sum of the distances between the mean and every point in the right is = 2+3+5+5+11+14 = 40
As you can see the distances add up 40 therefore the distribution is balanced at its mean.