Weighted Average with
denominator 7, or
wa7, is calculated using the formula:
wa7 = ((value + (6 * l_wa7))/7)
l_wa7 = last wa7 value
About 99% of "wa7" value is derived from the last 28 values (a month of daily values) and about 66% of "wa7" value is derived from the last 7 values (a week of daily values). Its main purpose is to smoothen the variation between the daily value, so that it is possible to see whether the current daily value is more or less than the weighted average of the past week or so.
The following example calculation of "wa7" over a number of days for Pseudo_Intellectual's XP shows how "wa7" smoothens the variations in daily increases of P_I's XP.
mm/dd XP wa7 inc
05/02 9004 - -
05/03 9164 160 160
05/04 9393 170 229
05/05 9453 154 60
05/06 9510 140 57
05/07 9577 130 67
05/08 9736 134 158
05/09 9833 129 97
05/10 10110 150 277
05/11 10242 147 132
05/12 10299 134 57
05/13 10370 125 71
Clearly, it can be seen that P_I's increase on May 13, 2000 is much below (about half of) the weighted average over the past few days.
If you analyse the "wa7" formula, you can see that the weightage for each value making up the current wa7 value, is 66% from the first 7 (week's) values, and 99% from the first 28 (month's) values.
Today = 14.3% = 1/7
Today-1 = 12.2% = (1/7)*(1 - 1/7)
Today-2 = 10.5% = (1/7)*((1 - 1/7) - (1/7)*(1 - 1/7))
Today-3 = 9.0%
Today-4 = 7.7%
Today-5 = 6.6%
Today-6 = 5.7%
--- Total to end of 1st Week = 66.0%
Today-7 = 4.9%
Today-8 = 4.2%
Today-9 = 3.6%
Today-10 = 3.1%
Today-11 = 2.6%
Today-12 = 2.3%
Today-13 = 1.9%
--- Total to end of 2nd Week = 88.4%
--- Total to end of 3rd Week = 96.1%
--- Total to end of 4th Week = 98.7%
See also: statistics, Statistics every writer should know, Discussions with /dev/joe on weighted average