Hi All,

I've been working on a formula where if I take the mean of three variables, mean value not be larger or smaller by 25% of any of the three variables. I've come up with a formula given that I have values for two of the variables V1 & V2 but not the third V3.

To solve for V3

Upper Limit Formula
Mean = (V1 + V2 + ((Mean/0.75))/3
3Mean = V1 + V2 + (Mean/0.75)
(3Mean) - (Mean/0.75) = V1 + V2
2.25Mean - Mean = (V1*0.75) + (V2*0.75)
Mean = ((V1*0.75) + (V2 * 0.75))/1.25

Solve upper V3
Mean = (V1 + V2 + V3)/3
V3 = (3*Mean) - V1 - V2

Lower Limit Formula
Mean = (V1 + V2 + (Mean/1.25))/3
3Mean = V1 + V2 + (Mean/1.25)
(3Mean) - (Mean/1.25) = V1 + V2
3.75Mean - Mean = (V1*1.25) + (V2*1.25)
Mean = ((V1*1.25) + (V2 * 1.25))/2.75

Solve lower V3
Mean = (V1 + V2 + V3)/3
V3 = (3*Mean) - V1 - V2

The formula works perfectly for multiple V1 & V2 values such as V1 = 102 & V2 = 108 but does not for the upper value when V1 = 100 & V2 = 110 and I can't seem to understand why or how to account for it. The lower limit formula always works.

Thanks

 

There is only one way to calculate the mean of n variables. Imposition of arbitrary constraints on the value of the mean seems like a dubious proposition to me. I don't think it is possible. Also, does you lower limit formula continue to work if negative values are allowed?

 

I've been working on a formula where if I take the mean of three variables, mean value not be larger or smaller by 25% of any of the three variables.

This is not mathematically possible.

Try v1=1 and v2 = 10

The mean of the three would have to be less than 1.25 and greater than 7.5.