A weighted average multiplies each data point by an arbitrary 'weight' and divides by the sum of the weights. Your everyday garden variety average, or arithmetic mean, is actually a special case of a weighted average, except all the weights are equal to 1.

X= 4

Y = 8

AV = 6

4---6---8

Notice the distance to average from both sides are the SAME (2)

Now let's find the average of 4, 4, 4, 8

AV = 20/4=5

4..5........8

Now if you notice the distance between 4 and AVERAGE is 1 and the distance between 8 and AVERAGE is 3

since we used 3 fours our average shifted close to the 4.

if you compare the distances

4...L...5....3L.....8

L/3L = 1/3 gives us the weights of the each term in a reverse proportion:

from this distance information you can conclude

3 fours
1 eight

Play around with this concept and you will find it very useful in many mixture and average questions.

Happy studying,