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 W 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; t Partipipating Nuxnbex- of Districts is a unit of for county tax rate of xation, and . (2) KRS, ‘ G. 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. ’ ' to “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. 9 _,. 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 ti (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 (1 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 IR 9 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