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What is a weighted moving average and how is it calculated? 

Weighted moving average explanation with chart examples and formula
Weighted average of world population from 1982 to 2010
You can see the world population data below together with the alarming growth rate. Below it is the 4 period weighted moving average of it.
The colour coding is used to show how the calculations are made. The first four periods are 4.59, 4.75, 4.92, 5.09 now we will look at the calculation.
It is more complex than the calculation of the simple moving average as it "weights" more on the most recent data and "fades" the older data.
The calculation is shown below.
Period 1 (4.59 x 1 ) + Period 2 (4.75 x 2) + Period 3 (4.92 x 3) + Period 4 ( 5.09 x 4) = 49.21 then we divide this by the sum of the data x multiplier. Which is 1+2+3+4 = 10 which gives us 4.92 as a four period weighted average.
So to explain what is happening I will start at the beginning. The first period used is always = to itself which is the same as multiplied by 1. The second period is multiplied by 2 The third period is multiplied by 3 The fourth period is multiplied by 4.
Once we have them multiplied up, we add all the multiplier used up together thus 1 + 2 +3 +4 = 10. So the number 10 will be our divisor which we use to divide the total of Period1 x 1 + Period2 x 2 + Period 3 x 3 + Period 4 x 4.
The correct mathematic statement for this would be ( (4.59 x 1 ) + (4.75 x 2) + (4.92 x 3) ( 5.09 x 4)) / 10 Please note there are double brackets around the formula above. Basically this means you will do the small calculations first and then the final division by 10 is the last step.
The next stage in creating a weighted moving average is to roll forward to the right by 1 number. So for the next value we will use Period 2 ,3, 4, 5, 6
Key points to remember
In the next example we shall use a 6 period weighted moving average.
Weighted average of USA unemployment figures from 1998 to 2012
As before we are going to start by multiplying period 1 by 1 and then move across from left to right adding 1 to the multiplier in each step. Thus...
Period 1 (4.50 x 1 ) + Period 2 (4.20 x 2) + Period 3 (3.90 x 3) + Period 4 (4.6 x 4) + Period 5 ( 5.8 x 5 ) + Period 6 ( 6.2 x 6 ) = 109.2 then we divide this by the summation of all multipliers. Which is 1+2+3+4+5+6 = 21 which gives us 5.20 as a six period weighted average.
The calculation is then shifted one data point to the right so for the 2nd value we use the following...remembering that the first value is multiplied by 1.
Period 2 (4.20 x 1 ) + Period 3 (3.90 x 2 ) + Period 4 (4.6 x 3 ) + Period 5 ( 5.8 x 4 ) + Period 6 ( 6.2 x 5 ) +Period 7( 5.4 x 6) = 112.40
Again we divide this by he total of all the multipliers which is 1+2+3+4+5+6 = 21 which gives us 112.40 divided by 21 = 5.35.
Mathematical symbol for weighted average
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