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points E,F and G are plotted on a number line at -1, 2 and 6 respectively. Find the coordinate o f the point that represents the weighted average of E, F and G, if point E weighs twice as much as point F and point G weighs three times as much as point F.

User Robottobor
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Answer: 3 is the weighted average

Explanation:

A weighted average is sort of like it sounds. - Different data-points are given different weights as far as how much they affect the answer. It's like you had 4 people on a corporation's board and all four get to vote, but their votes count differently. Person A has a vote that counts as 3. Person B has a vote that counts as 2 votes. Persons C & D each have a vote that counts as just one vote. For peron A to get outvoted, all the others must gang up against him.

Okay, back to our actual problem ...

  • point E measures (-1) and has weight 2x weight of F
  • point F has a measure of 2 and no particular stated weight
  • point G measures 6 and has a weight of 3x weight of F

Since we can assign a weight to point F and the other weights will be based on that, let's just keep it simple and give point F a weight of 1.

That gives E a weight of 2, and G a weight of 3.

So, ...

E value times E weight is (-1) x 2 = -2

F value times F weight is 2 x 1 = 2

G value times G weight is 6 x 3 = 18

Sum of (value x weight) = 18

Sum of the weights = 2 + 1 + 3 = 6

WE get the weighted average by taking the sum of (value x weight) products (18) and then dividing by the sum of the weights (6).

18/6 = 3, the weighted average

The point at coordinate 3 represents the weighted average.

User Artun
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