The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the distribution balanced?

Respuesta :

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.

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