xt7bzk55hz37 https://exploreuk.uky.edu/dips/xt7bzk55hz37/data/mets.xml Kentucky. Department of Education. Kentucky Kentucky. Department of Education. 1946-10 bulletins English Frankford, Ky. : Dept. of Education This digital resource may be freely searched and displayed in accordance with U. S. copyright laws. Educational Bulletin (Frankfort, Ky.) Education -- Kentucky Educational Bulletin (Frankfort, Ky.), "The Appropriation, Distribution and Administration of the State Equalization Fund", vol. XIV, no. 8, October 1946 text
volumes: illustrations 23-28 cm. call numbers 17-ED83 2 and L152 .B35. Educational Bulletin (Frankfort, Ky.), "The Appropriation, Distribution and Administration of the State Equalization Fund", vol. XIV, no. 8, October 1946 1946 1946-10 2022 true xt7bzk55hz37 section xt7bzk55hz37 (I
I

a“ __\y

’T 7:: rarian

N “P_

I
I
I
I

a. riouich-

i'entucky

0 Commonwealth of Kentucky 0

EDUCATIONAL BULLETIN
_

THE APPROPRIATION, DISTRIBUTION
AND ADMINISTRATION OF THE
STATE EQUALIZATION FWD

:3 i"
X

n:- Isiv F‘f‘itf’
35fo 1‘. :‘L-‘I’l,

Published by

DEPARTMENT OF EDUCATION

T JOHN FRED WILLIAMS
Superintendent of Public Instruction

ISSUED MONTHLY

Entered as second— class matter March 21, 1933, at the post office at
Frankfort Kentucky, under the Act of August 24,1912.

VOL. XIV October, 1946 No. 8

FOREWORD

This bulletin deals with the methods used in apportioning the
equalization fund. It gives the procedures used in calculating the
amounts due each district. It is hoped that the data presented and
the procedures used will serve to answer many questions concerning
the administration. of the equalization law. You are invited to study
this bulletin so that you n‘lay share with us your experiences in any
attempt at further improvement in the equalization law. It is our
hope, as you well know, that a larger number of districts may partici-
pate in the equalization fund as our total state appropriations in-
crease, and that, through the increase in the equalization fund, We
may be able to provide more adequate school. services for all the chil-
dren of the Commonwealth.

This bulletin was prepared by J. D. Falls, Chieic of the Bureau Of
Finance.

JOHN FRED WILLIAMS

Superintendent Public Instruction
October, 1946

19; the
1g the
d and
arning
study
1 any
s our
Lrtici-
S in-
l, we
chil-

III of

THE APPROPRIATION, DISTRIBUTION AND. ADMINISTRA-
TION OF THE STATE EQUALIZATION FUND FOR
THE PUBLIC SCHOOLS OF KENTUCKY

It is a truism known to every thinking citizen of Kentucky, that
there are wide differentials in the amounts of recurring revenue back
of each pupil. in the various school districts of the State. These dif-
ferences are due largely to the variations in assessed valuations and
the rates of the tax levies in the different school districts. To illus-
trate, each census child in \Voodford County, 1944-45, had $10,717 of
assessed wealth behind him, while the taX rate was only 30 cents on
the $100. At the same time, each census child in Clinton County had
only $408 behind him, and the tax rate was 75 cents which was then
the legal maximum limit for general purposes. For that year, the
mean average amount of assessed property for all the 257 independent
and county school districts, was $2,267 with a range of $10,309. Thus,
most of the less able county districts were putting forth two and a
half times more fiscal. effort than the more wealthy Woodford County
district, and yet, they were collecting less per child. Obviously the
children living in the richer districts have much better educational
opportunities than those living in the less able districts. Therefore,
knowing these conditions existed, the citizens of the State determined
to make some amends.

In the year ending June 30, 1941, each school district received
only $12.33 for each census child (from six to seventeen years of age
inclusive) within its jurisdiction, which was the only state aid then
available, other than that received from the Federal Government for
vocational programs. So, in November, 1941 an amendment to the
State Constitution received a favorable vote of the people, to permit
the distribution of not more than ten per cent of the Common School
Fund on bases other than per census. This enabled the 1942 General
ASSembly to make an appropriation and enact legislation to set up an
0Qualization law whereby the less able school districts could receive
additional aid from State sources.

The first equalization fund so appropriated was for the school
year of 1942-43, which amounted to $400,000, and was distributed to
SIX independent and thirty-three county districts ; in 1943-44, the
amount was $400,000, and was distributed to five independent and
thll‘ty-two county districts; in 1944-45, the amount was $1,500,000 and
distributed to eighteen independent and sixty county districts; in

561

pendent and fifty—seven county districts; and for the school year of
1946-47, the amount is $1,850,000 distributed to thirty-nine independ.
ent and fifty—one county districts. Table 1 shows a detailed tabula-
tion of these data for the five years the equalization law has been in
force.

Table 1

Table Showing Total Average Daily Membership, Net and Adjusted Re-
curring Revenue, Actual Equalization Distributed, Minimum
Legal Limit, Mean Average Revenue Per Pupil, Mean
Average Equalization Per Pupil, and Number
of District Participating

1945-46, the amount was $1,500,000 and distributed to twelve inde-

Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Item 7 Items
Q)
Mini— N 5,95 g!
Average Total mum h..._. H"
School Daily Total‘Net Equalization Legal mi ~l~ 0:335. Egm
Year Member- Recmring Actually Limit :1 ”if. {E :1 emf,
ship Revenue Distributed Per (15:14“ :EQ‘N ﬁg:
Pup“ étzrﬁ $323+ sat
Emil-.8 END-(<4 ZN:
| |
1942—43 165,775 $1,332,126.005ﬁ 399,999.24 $30.00 $28.55 $2.41 39
1943-44 147,539 3,899,363.84 399,999.79 30.00 29.14 2.71 37
1944-45 242,492 7,281,246.57 1,499,855.96 40.00 36.21 6.19 68
1945-46 219,857 6,899,410.75 1,499,973.41 40.00 38.20 6.82 59
1946-47 1204,574 29,044,076.46 1,850,000.00 “none 53.25 9.04 90

1 ADM + ADA is provided under the current equalization law, as a unit of
( 2 distribution.

2This is ”adjusted" and other recurring revenues which include for county
districts only the amount that would have accrued, if collected at a tax rate of
75 cents per $100 of assessed valuation of property subject to local taxation, and
graiﬁindependent districts, if collected at $1 per $100. See Section 157.051 (2) KRS:

3 The present law fixes no limit See Section 157.053 (2) KRS, 1946.

Table 1 may be read as follows: In 1942—43 there were 165,775
(Item 2) pupils in average daily membership (ADM) in all the par-
ticipating school districts. These districts collected a total of $4,332'
126 net recurring revenue (Item 3). The amount in equalization
actually distributed was $399,999.24 (Item 4). A minimum limit of
$30 (Item 5) per pupil was fixed by law, but since the appropriated
amount of $400,000 was not sufficient to guarantee the $30 limit, the
money was distributed on a ratio or percentage basis according to law.
This placed an average of $28.55 in local and State revenue (Item 6)
back of each pupil instead of the $30 minimum. That same year
when the equalization fund was distributed there Was a mean ayerage
of $2.41 in equalization fund (Item 7) prorated by the State to each
pupil in average daily membership in those 39 school districts partic-

562

;welve inde-
1001 year of
e independ.
iled tabula.
has been in

Iljusted Re-
umum
an

I 7 Item;

Partipipating

Nuxnbex- of
Districts

is a unit of

for county
tax rate of
xation, and
. (2) KRS, ‘

3 165,775
the par-
? $4,332,-
.alization
limit of
'opriated
imit, the
g to law.
Item 6)
me year
average
to each
; partic-

ipating. 1n the school years of 1943-44, 1944-45, 1945-45, marked
increases in equalization appropriationsare shown.

Further, Table 1 shows that in 1946-47 there was an average of
204,574 pupil units in average daily membership (ADM) and average
daily attendance“ (ADA). This average of pupil-units is obtained
by dividing the sum of ADM and ADA by two, according to Section
157.051 (3) KRS, 1946. In 1946-47 the amount of “adjusted” and
other recurring revenues from local and State sources is $9,044,076.46
and the equalization fund is $1,850,000. The sum of these two revenue
funds distributed among the 90 participating school districts guaran-
tees $53.25 back of each of the 204,574 pupils represented as being
in average daily membership and average daily attendance; and places
a mean average of $9.04 in State equalization revenue back of each
of these “average pupils” or pupil-units in the 90 districts.

EQUALIZATION LAW ENACTED IN 1946

In order that the 1946 Equalization Law may function more ef-
fectively, those whom it concerns should become thoroughly familiar
with it; and know how it applies to the common school system of the
State. ’ Therefore it is quoted below in its entirety:

157.051 Deﬁnitions for KRS 157.052 to 157.055. As used in
KRS 157.052 to 157.055:

(1) “Equalization fund” means a. special fund of ten percent
of the total appropriation for common school fund, appropriated by
the General Assembly for the specific purpose of equalizing education
service in the less able local school districts of Kentucky.

(2) “Adjusted recurring revenue” means all recurring revenue
other than that produced by a subdistrict tax and that received by a
school district from the equalization fund; provided that in a county
school district only the amOunt of ad valorem revenue is included
that was accrued at the tax rate of seventy—five cents per one hundred
dollars of assessed valuation of property subject to local taxation, and
that in an independent school district only the amount of ad valorem
revenue is included that was accrued at the tax rate of one hundred
cents per hundred dollars of assessed valuation of property subject to
local taxation.

(3) “Arithmetic mean index” means the quotient obtained
when the sum of the average daily membership and the average daily
attendance in a school district is divided by two.

\
L ”.The 1946 law added zivel'ﬂg'e daily membership '11-“: another factor in the
Hstribution of equalization funds.

563

Hip,» ~.,_,_., .. 4; -‘

(4) “Net—ability index” means the quotient obtained When the
total adjusted recurring revenue of a school district is divided by the
arithmetic mean index.

157.052 School equalization fund distribution, who to make.

The equalization fund shall be distributed and administered
under the direction of the Superintendent of Public Instruction, with
the approval of the State Board of Education, as provided in KRS
157.053 to 157.055.

157.053 Eligibility for aid from equalization fund; how deter-
mined; annual study; ranking of districts; basis of distribution.

(1) Any board of education that has had its budgets and salary
schedule for the ensuing school. year approved by the State Board of
Education, whose ratio of assessed valuation of property to fair cash
value is equal to the average ratio throughout the state, as certified
to the State Board of Education by the Kentucky Tax Commission,
and has levied for school purposes a tax of at least seventy—five cents
on each one hundred dollars of property subject to local taxation and
not less than the ad valorem tax levy made for the previous school
year, shall have the privilege of applying for aid from the equalization
fund.

(2) The Superintendent of Public Instruction shall make a
careful study to determine annually the amount of adjusted recurring
revenue that is available for the education of each pupil based on
average daily membership and average daily attendance in the publiC
schools in each school district in Kentucky. This study which shall
be used as a basis for the distribution of moneys from the equaliza-
tion fund, shall be based upon records and reports for the school year
ending June 80 immediately preceding such study. After all scl1001
districts in the state have been arranged in a rank order from high to
low according to their net-ability indices, the Superintendent of
Public Instruction, with the approval of the State Board of Educa-
tion, shall distribute the equalization fund to districts qualifying
under KRS 157.051 to 157.055 so that, when the total adjusted re-
curring revenue of all participating districts plus the total equaliza-
tion appropriation is divided by the total arithmetic mean indices of
all participating districts, it will give the same amount of money pel'
pupil per year represented in the arithmetic mean index in each par-
ticipating school district.

564

d when the
ided by the

:0 make.

lministered
iction, with
ad in KRS

how deter-
ibution.

and salary
: Board of
) fair cash
s certified
>mmissio11,
-five cents
:ation and
)us school
ualization

i make a
recurring
based on
he public
1ich shall
equaliza-
hool year
all school
n high to
ndent of
E Educa-
1alifying
1sted re-

equaliza-

1dices of

)ney per

ach par-

157054 Time of allotment and distribution of equalization
fund.

The special l'uud shall be allotted to the. local boards ol’ education
which meet the provisions oi? KRS 157.052 to 157.055 by the Superin-
tendent 01’ Public instruction with the approval of the State Board
of Education on or before April 1, prior to the beginning of each
school year except: in 1942, when such allotment shall be made 011 or
before June l. The funds so allotted shall be distributed to the local
boards of education regularly as a supplement to the state per capita
funds provided for such districts.

157.055 Administration and expenditure of equalization fund;
rules for ,- liability for.

The Superintendent of Public Instruction with the approval of
the State Board of. Education shall prescribe rules and regulations
governing the administration and expenditure of any moneys allotted
to local school districts from this special fund. The money allotted
to any local board of education under the terms of KRS 157.052 to
157.055 shall be received and held and expended by it under the same
liability and responsibility as provided by law for other funds which
come into the hands of such board.

157.060 Reports of funds received and spent by school districts.

The officials of each educational institution and each school dis-
trict supported in whole or in part from taxation shall make a report
to the State Board of Education at the close of each scholastic year,
showing in detail all funds received from the state and from all other
sources during the year, and a detailed statement of all expenditures
for the year.

LEGAL TERMINOLOGY

The definitions set up in the 1946 law clarify the procedure and
give to local, school administrators information that will enable them
to know and understand better how the money is distributed. Further
illumination may not be amiss:

1- “Adjusted recurring revenue” is a necessary term. For ex-
' ample a county school district levying, say, $1.25 for general
purposes will have its ad valorem revenue “adjusted” so

as to charge it only with that portion of recurring revenue
that would have accrued, had the tax levy rate been fixed at »
only 75 cents; or, if an independent district levies $1.50, its

ad valorom revenue will _be “adjusted” to that. portion that

565

would have accrued, if it. had been collected at a tax levy
rate of $l. Hence, the term, “adjusted recurring; i'evenue”4
is used to explain this process of adjusting ad valorem rev.
cnue from the ratio of actual collections to the ratio for cal-
culations fixed by the law. The difference between the
rates of 75 cents for county and $1 for independent districts
was considered as a just differential because county districts
have the additional heavy expense of pupil transportation.
It is estimated that, where the purchase, operation and
maintenance of busses are considered, this differential is
reasonably commensurate. ’ '

“Arithmetic mean index” corresponds to the term, “pupil”
or “child” in the previous law. But, since this law gives the
same weight to attendance as to membership, the ADM and
ADA are added and divided by two to represent an average
pupil—unit in membership and in actual attendance. This
places emphasis where it should be. Since this 1946 law
uses these two terms instead of one, as in the previous law,
the mean average is used as a pupil-unit for determining the
basis of proration. In effect, this combines census, member-
ship and attendance so as to locate the child in the commu-
nity, get him in school, and encourage keeping him there.

3. “Net ability index” is merely the adjusted ad valorem and
other recurring revenue of a district, divided by the “aver-
age” number of pupil-units in membership and in actual
sehool attendance. This index indicates the amount of local,
per capita and other state revenue back of each “average”
pupil-unit in that district before equalization revenue is
applied.

SOME COMPARISONS BETWEEN THE OLD AND NEWVLAWS

Herein certain comments are submitted in explanation of the
pertinent changes made by enacting the 1946 law, regarding the diS-
tribution of the State equalization funds.

Fundamentally, the new law of 1946 is similar to the previous
law. However, certain factors have been incorporated which improve
and simplify the law. These changes are so made that it will not be
necessary to rewrite the law every two years, as was necessary before-
The derived formula. will distribute any appropriated amount accu-

‘Revenue is additions to cash or other current assets which do not increase,
any liability, nor represent the recovery of an expenditure. But “recurring ”WM!“
is that which is normally collector] and expected from time to time and on "1'
definitely.

_,__'4
._,_._

a tax levy
.‘ revenue’u
alorem rev.
,tio for cal.
etween the
111‘; districts
ty districts
Sportation.
'ation and
erential is

“ pupil”
,7 gives the
ADM and
n average
lee. This
1946 law
'ious law,
ining the
member-
: commu-
there.
trem and
e “aver-
n actual
of local,
verage”
'enue is

LAWS

of the
the dis-

revious
nprove
not be
before.

accu-

ncrease

avenue”
on 1n-

ratcly,

whether it be one million or ten million dollars. Some of the

weaknesses in the old law are presented below:

1.
2.

It had to be rewritten every two years.

It set up an amount of $30, or $40 per pupil in aVerage daily
membership as a floor or minimum, But the amount so
fixed was always higher than the available appropriated
revenue could provide per pupil, because the exact appro-
priation could not be predetermined. Usually this mini-
mum was little better than a guess and therefore necessitated
the use of a ratio or percentage method, which still left
unequal the amount of local and state revenue back of each
pupil-unit.

The unit or base for distribution was the average daily
membership. If a pupil came to school only one day and
then dropped out for the remainder of the school year, there
was (under this old Law) just as much equalization money
allocated to that district for that pupil as would have been,
if that pupil had attended full time. Naturally, it is im-
portant that a child become a member of his school, but it is
also highly essential that he attend regularly.

Average daily membership was very little better than no
method at all. It may have been selected, at first, because
it was the easiest quantitative factor then obtainable and yet
objective in a way. Now, it is realized that average daily
attendance may be a better single measure, but that the com-
bination of membership and attendance is still more logical.

The 1946 law facilitates distribution, and will actually equalize
the amount of revenue (state and local) back of each “average” pupil
in all the districts participating. This money is distributed on the
basis of need ability, as indicated by data taken from the annual rec-
Ords and financial reports for the year immediately preceding the
year of calculation. For example, the equalization apportionment to
a participating distiict in 1946- 47, was calculated in 1945- 46, from
data that were obtained from the 1944- 45 official instruments which
were the last complete 1ec01ds on file. (See law quoted above).

METHOD OF DISTRIBUTING THE EQUALIZATION FUND

UNDER THE 1946 SCHOOL LAW

According to law, all dist1icts 1n the State ale listed in descend-
ing lank- -01 deI scale f1 0111 the highest “net ability index” to the low-

567

est.5 Then, the equalization revenue is simply prorated to the less able
districts beginning at the bottom of the scale and advancing up this
scale until all or 100% of the equalization revenue is distributed; and
also, at the same time, when the local adjusted ad valorem and other
recurring revenue in a district and equalization money are added, it
Will place the same minimum or total amount of money back of each
“average pupil’7 therein, as will be back of every other such pupil in
all the participating districts.

In order to meet this requirement. of the law and to ascertain
what districts, after meeting all other qualifications under the law,
may participate in the equalization fund, and also to determine what
their apportionments may be, the “CRITICAL REVENUE RATIO” must
be determined between the summation of the all adjusted recurring
revenue plus the equalization fund, and the corresponding cumulative
frequencies of arithmetic mean indices of all these districts partici-
pating. All data are to be taken from the reports of the fiscal year
ending June 30 immediately preceding the year in which calculations
are made.6

THE DERIVED FORMULAE

In order to simplify the procedure in deriving the formulae that
will precisely fix this critical revenue ratio, the following steps have
been taken:

Step 1. Divide by two the sum of each district’s average daily
membership and average daily attendance. This quo-
tient is called the Arithmetic Mean Index of that dis-
trict, which is the “average pupil” used as a unit for
distributing equalization fund.

Step 2. Divide the total. of the adjusted ad valorem and other
recurring revenue of each district by its own arithmetic
mean index. This quotient is called the Net Ability Ill-
dex of that district. See Table 2, Item 3.

Step 3. Rank the districts in descending order from high to 10W
according to their Net Ability Indiees. Then list 01"
posite each of these indices, the respective Arithmetic
Mean Index and its total amount of adjusted ad valOI‘em
and other recurring revenue. See Table 2, Items 3,4
and 5.

6 See Table ‘2; 'Itemli.

'See school law for definitions or terminology and procedures. _

568

the less able
ting up this
ibuted; and
n and other
re added, it
ack of each
ch pupil in

o ascertain
er the law,
rmine What
mo” must
1 recurring
cumulative
cts partici-
fiscal year
:alculations

.nulae that
steps have

rage daily
This quo-
? that dis-
1 unit for

and other
trithmetio
.bility In-

gh to 10W
1 list op-
rithmetic
l valorem
:ems 3, 4

(

Step 4.

Step 5.

Theoretically, one may begin at the bottom of these
rank—order districts and proceed upward to determine
by computation the first pain! on the ascending scale
of Net Ability ludiccs where the ratio of “Tentative
Cumulative Revenue,”7 is equal to or greater than the
Net Ability Index of the district last participating, but
less than the Net Ability Index of the next succeeding
district not participating. This will be the minimum or
the smallest revenue ratio that can be obtained and is
called the “CRITICAL OR TRUE REVENUE RA—
TlO.” Sec Step 5-b, below.

To explain in more detail, continue to divide the cumu-
lative frequencies of districts’ revenue plus total equali-
zation fund, by the respective cumulative frequencies
of aritlnnetic mean indices, until the ratios cease to
decrease and begin to increase. If these tentative cumu-
lative ratiOs are plotted, a rough parabola will result;
and the point of tangentS will be the smallest or mini-
mum ratio which is determined as follows:

(a) From the bottom of this scale of rank-order dis-
tricts begin adding the adjusted recurring revenue
in one column and the corresponding arithmetic
mean indices in another. (See Table 2, Items 5 and
7)

(b) Practically, it is not necessary to begin at the bot-
tom of the scale as in Step 4, but by inspection, one
may begin at any logical point to divide the cumu—
lative frequencies or summations 0f Adjusted Re—
curring Bevenue plus the equalization fund, by the
cumulative frequencies or summations of the corre-
sponding arithmetic mean indices. These quotients
are called “tentative revenue ratios” which will
become less and less until the minimum or CRITI-
CAL OR TRUE REVENUE RATIO is deter-
mined. After that point is reached, then, if such!
divisions are continued up the scale, the quotients
or revenue ratios will begin to increase slightly and
gradually. ‘

7 In ascending the scale, the mean indices and Cumulative Frequencies are the
gums obtained each time that another district’s revenue is added to the cumulative
re(luenmes of all preceding districts plus the total appropriated equalization fund.
See Table 2, Items 5 and 7.

i‘See graph. 574-75.

'0. . -_ .f.‘.e.v«);-rl-:;z - g:

(c) The minimum revenue ratio that becomes equal to
or greater than the last reSpective net-ability in-
dex, considered, but less than the next succeeding
net-ability index, will be the CRITICAL 0R
TRUE REVENUE RATIO” by which all appor-
tionments will be made, and will determine the
last district participating. (This CRITICAL OR
TRUE REVENUE RATIO should be carried out
to eight or more decimal places to insure the en-
tire distribution of the appropriated equalization
fund.)

Step 6. Multiply this “CRITICAL OR TRUE REVENUE RATIO” by
the arithmetic mean index of each district, 'subtract
from this product the district’s corresponding recurring
revenue, and the remainder will be the apportionment
of equalization fund going to that district.10

This procedure will distribute all of the equalization fund; and
each “average pupil” in each district, represented in the arithmetic
mean of the average daily membership and the average daily attend-
ance, will have the same total amount of local and State revenue be-
hind him that is indicated by the “CRITICAL OR TRUE REVENUE
RATIO.” This conforms to Section 157.053 (2) KRS, 1946.

Staying away from technical mathematics in these explanations,
it can be stated briefly that the principles evolving these formulae, are
based on two theorems developed through certain equations:

1. The summation of the products of the quotient multiplied
by each of the various parts of the divisor, Will equal the
dividend.

_,. The point of tangent of the rougli parabola formed in graph-
ing the “tentative revenue ratios” of the various school dis-
tricts, to the verticle side of the rectangular graph depicting
the total. revenue back of each pupil, is the minimum or criti-
cal revenuc ratio that will distribute all of the equalization
fund. See Table 2, Item 8; and Graph.

Avoiding technical phrasing, the statements of these theorems

may be somewhat loosely worded, but their meanings seem reasonably
clear and obvious.

9See formula 11-c, also Table 2, Item 8.
1° See formula. 12-a, and c.

qu‘al to
.ity in.
:eeding
L 0R
appor-
ne the
LL OR
ed out
the en
ization

'0 ” by
thract
urring
nment

l ; and
1metic
ttend-
ue be-
VENUE

,tions,
e, are

iplied
Ll the

mph-
1 dis-
cting
criti-
ation

reins
ably

THE DERIVED FORMULAE FOR DISTRIBUTING
THE EQUALIZATION FUND

M is symbol for average daily membership in a district
d

A is symbol for average daily attendance in a district
1‘]

I is symbol for arithmetic mean index of a district
dis

P9599!“

SI is symbol for summation or the cumulative frequencies of
d

all participating districts’ arithmetic mean indices
R is symbol for total adjusted ad valorem and other recur-
d

CI!

ring revenues of a district
6. SR is symbol for summation or the cumulative frequencies
d

of all participating districts’ recurring revenue
7. E is symbol for total state equalization fund
1

8. Edis symbol for the amount of equalization fund going to a

district
9. S is symbol for “summation of”
10.] R is symbol for the critical or true revenue ratio

11. The Critical Ratio Formula or Equation

(a) (SR + E) = total local and state revenue plus total
a ‘ equalization appropriation
(b) M + A
S (l—2—4) :2 SI , summation of or cumulative frequen:
“ cies of pupils in all participating dis-
tricts.
(0) Therefore:

(sad + E)
m =R, Critical ratio or minimum ratio be-
( d d) “ tween the total revenue and the total
S 2 —* number of these pupils in participating
districts.
M + A
(d) Since, S 312*? : SI
Then, (SR + E)
s1 = R:

a
’The smallest or minimum revenue ratio obtained from these divisions will

318 tthe “CRITICAL OR TRUE REVENUE RATIO" to be used in making the final
5 “b“UOD 0f the Equalization Fund going to each district.

571

(e) By substituting actual values:

$9 044 076 46 + $1, 850, 000
204,574

.a —$53. 25249767, the total rev-
enue back of each of these
pupils.

12. The Formula or Equation for Determining District’s Ap-
portionment

(a) (M M+_ A SR + E) ‘
(M531 —Rd__ — E, apportionment of

equalization going
to each participat
ing district

, SR + E
(13) BM, M : I , and (—L—J) : R
2 d SI c

(o) By substituting in (a)
I x R — R = E

By substituting in (0) actual values, say, for Webster
County:

1600 x $58.25249767 —— $84,956.21 : $247.79* apportion-
ment to Webster County

The graph 011 pages 574—75 illustrates how one may follow the
procedures in ﬁnding the Critical Ratio used in making the distribu—
tion of the equalization appropriation. Obviously it is not necessary to
begin actually calculating the tentative revenue ratios at the WW
bottom of the scale; but wherever one begins, the preceding cumulative
frequencies must be taken into account. The graph as well as TableZ
illustrates the theoretical procedure. By inspection, one may estimate
that the last qualifying districts would fall in the upper eighties 01‘
lower nineties on this particular scale. However, it is very necessary
when the calculations approach the critical or minimum revenue
ratio, that each district be examined separately and carefully to in-
sure that the smallest or minimum revenue ratio will be found.

In making this study, it was not necessary to rank all the 256 diS-
tricts in a single table to determine those that were qualified under
this Act. However, a sufficient number above was considered to in-
sure that no qualified district would be omitted. For the purpose 0f
making this study, the net-ability indices of all districts in the State

‘ See Table 3, Items 4, 5, 6 and 7.

total. rev.
h of these

trict ’s Ap.

)nment of
,tion going
participat,
net

Webster

pportion-

)llow the
distribu-
essary to
:he very
mulative
Table 2
estimate
mm or
ecessary
revenue
v to in-
l.

256 dis-

l. under
1 to in-
pose of
e State

e i
were calculated, but only 105 districts were actually ranked in a pre— l
liminary table according to their net—ability indices. The net-ability , .
indices of these 105 districts spread from $33.67 for Gatliff Inde- 3'
pendent District to $58.37 for Marshall County District. It so hap- v
pened in this instance that there were only 90 of these districts that ‘ .
actually qualified. But, for the purpose of illustrating further the ‘
method of calculating and reducing the number of operations to a
minimum, these 90 districts have been thrown into step-intervals of
five, except for the first five districts, and the last five districts in
the scale to insure finding the exact critical ratio.

It should be definitely understood that each district near t