FOREST TAXATION IN THE UNITED STATES 125 
TABLE 39.—Ezample showing method of calculating the coefficient of dispersion 
Assessed ASS€SS- ang 
Assessment group sles True value TiGnGeatiO Deviation ! 
PASS eit LL PARTS SE A SE Le a kd , 000 = 
BS PR a ale Sa eA 1, 100 2, 000 55 115 300 
© ae rE SS Aik Ne 2) gee She Oe 7, 200 10, 000 72 +2 200 
) D a yep eae es eee AL eee ene Pan ey ee 6, 000 8, 000 75 400 
TES ee SOE NS Se hE LE ON ee Eee 5, 400 6, 000 90 +20 1, 200 
‘ WN 
Coefficient of dispersion=—5= 17 percent. 
1 Individual deviation percent equals individual ratio minus average ratio; this percentage (ignoring 
signs) times true value gives deviation in dollars. Flee 
31 Total assessed value divided by total true value, 31.000 =70 percent, average assessment ratio. 
3,600 pane 
8 Total deviation divided by total true value, a= 12 percent, average deviation. 
The coefficient of dispersion for a group of properties (when com- 
puted from an average deviation that is weighted by value) has the 
advantage, not only of being a measure of variation in assessment, 
but also of having a definite relationship to the portion of the taxes, 
levied at a uniform rate on the group, which is misplaced as the result 
of unequal assessment within the group. If the coefficient were 
precisely determined, it would equal twice the percent of misplaced 
tax. This may be readily understood from the facts that the total of 
deviations above the average assessment ratio is equal to the total 
of those below and that the tax on properties with assessment ratios 
above this average is out of place and should be paid on those prop- 
erties with assessment ratios below the average. A mathematical 
proof of this relationship follows. 
Let— 
D=coefficient of dispersion, defined as the ratio of the average 
deviation of individual assessment ratios weighted by 
true values to the weighted average assessment ratio of 
the entire group, 
11, ¥2,...U,=the true value of each individual property in the group, in 
which n is the number of properties, 
@1, G2, .- - dn=the assessed value of each individual property in the group, 
T=the total tax, 
M=the amount of misplaced tax (aggregate tax transferred 
between properties by inequalities in assessment ratio), 
t=tax rate which applied to the total assessed value gives the 
required total tax, 7, 
t’=tax rate which applied to the total true value gives the 
required total tax, T, 
11, T2,-.+Tn=the assessment ratio for each individual property in the 
group, 
: k=the average assessment ratio (weighted by true values), 
or aggregate assessed value divided by aggregate true 
value, times 100. 
The problem is to prove that M =5 D-T. 
The average deviation of assessment ratios, weighted by true values, is deter 
mined by multiplying the absolute difference between each individual assessment 
ratio and the average assessment ratio by the true value of that individual prop- 
