
62 N.J. 203 (1973)
300 A.2d 129
THE TOWNSHIP OF WILLINGBORO IN THE COUNTY OF BURLINGTON, PETITIONER-APPELLANT,
v.
THE BURLINGTON COUNTY BOARD OF TAXATION, RESPONDENT-RESPONDENT.
The Supreme Court of New Jersey.
Argued May 2, 1972.
Reargued December 4, 1972.
Decided January 29, 1973.
*206 Mr. John S. Fields argued the cause for petitioner-appellant (Messrs. Bookbinder, Fields and Ferri, attorneys).
Mr. Richard M. Conley, Deputy Attorney General, argued the cause for respondent (Mr. George F. Kugler, Jr., Attorney General, attorney; Mr. Elias Abelson, Assistant Attorney General, of counsel).
Mr. Richard H. Saxe, Deputy Attorney General, amicus curiae, argued the cause at the reargument.[*]
Mrs. Ethel M.S. Yahnel (of the New York bar), amicus curiae, argued the cause at the reargument.[*]
*207 The opinion of the Court was delivered by CONFORD, P.J.A.D., Temporarily Assigned.

I. Introduction

This appeal concerns the county tax equalization table of Burlington County for the tax year 1970. The township of Willingboro complains that the final table prepared and certified by the Burlington County Board of Taxation assigned it an excessive share of the county tax burden of 1970 in relation to the shares assigned the other taxing districts of the county. The Division of Tax Appeals, after a hearing, dismissed Willingboro's appeal. The Appellate Division affirmed, relying upon its decision in Tp. of Little Falls v. Passaic County Bd. of Tax., 115 N.J. Super. 115 (App. Div. 1971), wherein the same general problem as is here implicated was presented and the court sustained a county tax equalization table as against objections similar to those here made by Willingboro. We granted certification. 60 N.J. 18 (1972).[1]
The factual issues presented are complex. Before detailing them it will be useful to expose the general nature of the basic problem. For purposes of securing an equal proportionate allocation among the taxing districts of a county of the cost of county government each county board of taxation is required by N.J.S.A. 54:3-17 et seq. annually *208 on or before March 10, on notice and opportunity to be heard to all municipalities therein, to determine "according to its best knowledge and information" the ratio or percentage of true value at which real property of each taxing district is assessed according to the local tax lists and to prepare an equalization table showing the aggregate assessed valuation of the real property in each district and the ratio or percentage, if any, by which the assessed valuation should be increased or decreased in order to correspond to the true value thereof, also stating such true value. For a thorough treatment of the history, interpretation and practical difficulties long encountered in administering this statute see City of Passaic v. Passaic County Bd. of Taxation, 18 N.J. 371 (1955).
The stated equalization function of the county boards does not in any way affect individual tax assessments against property owners. Those are required to be separately revised and corrected administratively by the county boards after receipt of the lists from the local assessors (N.J.S.A. 54:4-46, 47), and are subject to further revision and correction on appeal to the county boards and the State Division of Tax Appeals.
Practically total disregard by local tax authorities of the former statutory requirement of uniform assessment of all real property at true value (N.J.S.A. 54:4-1, as of prior to 1960) produced absence of any degree of uniformity within taxing districts of any particular ratios of assessment to true value, although unofficial ratios were frequently purported to be employed by many districts. City of Passaic, supra (18 N.J. at 378-382). Consequently it became difficult, if not impossible, for county boards of taxation literally to comply with the statutory duty, mentioned above, of determining accurately the ratios to true value at which local assessors were assessing. See In re Appeals of Kents 2124 Atlantic Ave., Inc., 34 N.J. 21, 26 (1961). This condition came gradually to be relieved by several developments: (a) the courts began to press for assessment *209 at true value, Switz v. Middletown Twp., 23 N.J. 580 (1957); Ridgefield Park v. Bergen Co. Bd. of Taxation, 31 N.J. 420 (1960);[2] (b) there was movement toward periodic, systematic revaluation of assessed properties, on a professional basis, spurred by decisions such as those just cited, by the activity of the local property tax bureau of the State Division of Taxation and by the disclosures of the Sixth Report of the Commission on State Tax Policy (1953); and (c) under compulsion of the requirements of the State School Aid Act of 1954, L. 1954, c. 85, N.J.S.A. 18:10-29.30 et seq. (now N.J.S.A. 18A:58-1 et seq.; 58-4), which provides for distribution to school districts of state financial aid determinable to some extent by the aggregate of the equalized realty assessments of the particular municipality,[3] the State Division of Taxation developed a useful system of determining fairly reliable municipal ratios of aggregate assessments to aggregate equalized true valuations based on analyses of prices in sales of property recorded. Such analysis entailed screening out such sales as were for various reasons not reliable indices of market value. The details of the basic method of sales analysis employed, with later variations which will in part be discussed hereinafter, are set forth in Bayonne v. Division of Tax Appeals, 49 N.J. Super. 230 (App. Div. 1958). Under well-warranted encouragement by the local property tax bureau of the Division of Taxation and the courts, see City of Passaic, supra, 18 N.J. at 385, most if not all of the county boards of taxation came to use the ratios of the Director of the Division of Taxation, promulgated for school aid purposes, as guides for purposes of establishment of the county tax equalization tables.
*210 It is the coincidence of periodic revaluation of assessments by municipal assessors and the reliance by the Burlington County Board of Taxation on the Director's municipal ratios for county equalization purposes which has produced the particular controversy involved in this appeal.
Aggregates of municipal equalized true valuations of real estate are fixed by the Director's table on October 1 of each year for purposes of the school fiscal year beginning the following July 1. Thus, in respect of the dates involved in the instant case, the Director's tables promulgated October 1, 1969 were fixed for application to state school aid for the school year July 1, 1970 to July 1, 1971. County boards of taxation, required to complete their county tax equalization tables by March 10 of the current tax year (in this case 1970), ordinarily use the Director's table of ratios of the prior year (in this case October 1, 1969) for their current tax year's county equalization tables. The Director's ratios are generally based on analyses of sales for time periods going back two years prior to the immediately preceding July 1 (in this case July 1, 1969). Despite this fact and the circumstance that the numerator of the fraction constituting the Director's ratio determinant consists of aggregate assessments for a year different from the current county tax equalization year, there is ordinarily no substantial impairment of reliability in the county board's use of the Director's ratios because, aside from new, enlarged or demolished structures, or general municipal revaluations or reassessments, etc., assessed valuations are largely repeated from one year's local assessment lists to the next.
The saving factor last above noted is, however, destroyed in relation to a taxing district like Willingboro which, along with several other districts in Burlington County, effectuated general revaluations for assessment purposes for the tax year 1970. It is apparent that a ratio arrived at by the Director by using assessed valuations for 1969 as the numerator of the fraction which is the ratio determinant cannot be applied for 1970 equalization purposes in the Burlington *211 revalued districts, consistent with proportionate treatment of non-revalued districts. As revaluations generally reflect accumulated increases in values since prior revaluations, the increases in aggregate assessments for 1970 in the revalued districts would cause gross distortion in the 1970 relative equalized valuations of such districts were the Director's 1969 ratios for the districts applied directly to their 1970 assessment aggregates.[4]
It is thus clear that a county board of taxation which is confronted in a given tax year with the circumstance that one or more, but not all, of the districts in the county have been revalued for assessment purposes, must apply a different mathematical formula to the new aggregate assessments of such districts if it desires to use the Director's school aid ratios of the prior October 1 in relation to equalization of the non-revalued districts. It will appear from the ensuing discussion that the Burlington County Board of Taxation failed to seek or find an appropriate formula in equalizing for the tax year 1970.[5]
Before setting forth the procedural background of the appeal and the specific fact situation presented it will facilitate comprehension of the issues if we outline the mechanics and the mathematics of the Director's ratios and of their ordinary use for county tax equalization purposes.
Sales for predetermined periods of time, usually for two years previous to the July 1 preceding the October 1 equalization date, are screened for valuation utility, and the usable sales are divided into four basic classes of property: vacant land, residential (four dwelling units or less), farm land, and all other (including commercial and industrial). The *212 current aggregate assessed valuations of the properties sold in each class are divided by the aggregate sales prices, yielding a ratio for the class. Each class ratio is divided into the aggregate assessed valuations for the class, yielding aggregate putative true valuations for the respective classes. These aggregates are added together, yielding the total putative true valuations for the district. These are ordinarily the operative figures for school aid distribution purposes. The aggregate assessments of the same tax and calendar year as the year of the Director's October 1 tables[6] are divided by the aggregate equalized true valuations last mentioned; this is called the average weighted ratio or weighted ratio (and we will hereinafter use the term "weighted ratio" therefor). Beginning with the Director's 1969 school aid tables, another ratio was developed, which we denominate the "final average ratio" (sometimes called "average ratio"). This is determined as follows: (1) take the aggregate equalized true valuations for the current year (as to the present case, 1969) and average them with the final aggregate true valuations certified in the Director's table for the prior year (i.e., 1968 as to the present case), the resulting figure representing the final certified true valuation for the current year; (2) the aggregate assessed valuations of the current year are divided by the final certified true valuations to produce the "final average ratio".
As is apparent, both of these latter ratios are only statistics insofar as distribution of school aid is concerned, see Bayonne v. Division of Tax Appeals, supra (49 N.J. Super. at 235), but they become operative when used for purposes of county tax equalization in the ensuing tax year.
*213 For county equalization purposes in the tax year following the filing of the Director's October 1 table some county boards use the Director's weighted ratio for the districts but most the final average ratios; in either case the county equalized true valuations are arrived at by dividing the current tax year's assessed valuations of the district by the ratio chosen. The higher the ratio for a municipality, the lower its equalized true valuations for the current tax year and the less its proportionate share of the cost of county government; and vice-versa.[7] But, as indicated above, the procedure set forth in this paragraph can be applied to a district only when there has been no general revaluation or reassessment of the district in the current tax year.

II. The Case Presented

Willingboro, formerly Levittown, had by far the greatest amount of 1969 and 1970 assessed valuations of realty of the forty taxing districts in Burlington County. About 99% of its individual real property assessment items is comprised of one-family dwellings of fairly uniform construction. In recent years, inclusive of 1969 and 1970, these have been sold at the rate of about one in five each year, and it is conceded that there has been a steady trend of increase in sales prices over that period, which continues. There was testimony before the Division of increases in building costs at the rate of 8 1/2% per annum. The assessor of Willingboro has maintained close study of the sales and has used a computer to update assessed valuations on all residences. Pursuant to this program there has been a general reassessment[8]*214 of ratables in Willingboro in each of the years 1968, 1969 and 1970
In 1970 ten of the taxing districts in the county (including Willingboro) effectuated reassessment or revaluation of their real property ratables, all presumably increasing them in the aggregate over previous years. For all of them except Willingboro the Director's October 1, 1969 weighted ratio and final average ratio were under 100, the weighted ratios varying from 52.23 to 88.22, the final average ratios somewhat higher. Willingboro's weighted ratio was 107.32 and its final average ratio 120.39.
Of the non-revalued districts, three, Lumberton, New Hanover and Wrightstown, had weighted ratios over 100, varying from 104.70 to 117.38 and final average ratios running from 107.48 to 130.27 (Lumberton). The other non-revalued districts had weighted ratios under 100.
In fixing its final equalization table for 1970, the county board set a ratio of 100 for every one of the ten taxing districts which had been revalued for that year, reasoning that since the legal standard of individual assessments for Burlington County fixed by the county board pursuant to N.J.S.A. 54:4-2.27 was 100% of true value, it should be conclusively presumed that the 1970 assessments on revaluation were based upon that standard. The board nevertheless used the Director's weighted ratios for those districts which had not revalued, except that as to those which had not revalued but had weighted ratios over 100, the official ratios were uniformly set at 100. It appears from the testimony of the secretary of the county board before the Division of Tax Appeals that "as a matter of policy" no district's county *215 equalization ratio would be fixed at in excess of 100 and that every one which revalued would be set at exactly 100. As an additional reason for fixing Willingboro's ratio at 100 the witness stated that Willingboro's assessor had certified the 1970 list as fixed at full true value. Before the Division, the assessor testified that the Willingboro 1970 assessments were at about true value, being based on studies of sales for the first eleven months of 1969. There was also evidence that spot checks of Willingboro sales in the first few months of 1970 showed a ratio of 1970 assessments of at or slightly below 100.
In summary, the county equalization table set the ratios of 27 districts at the precise weighted ratio of the Director's October 1, 1969 table, these all being under 100, varying from a low of 76.66 to a high of 97.72. The ratios of the other thirteen districts were set at the "policy" or presumed levels of 100, as indicated.
The position of Willingboro before the Division of Tax Appeals was basically that it was arbitrary for the county board to fix its ratio at 100 merely because it was attempting to assess at true value, without considering the relative current relationship to true value of the assessments of all the districts in the county inter sese; that from the latter standpoint the districts which had been assigned the Director's weighted ratios of October 1, 1969 (lower than 100) were receiving the benefit of calculations based upon the substantially lower average sales prices recorded during the sales-sampling period from July 1, 1967 to July 1, 1969 [except those for January 1 to June 30, 1968; see note 10 infra] used by the Director, as contrasted with average higher sales prices from January to November 1969 upon which Willingboro's revaluation for 1970 at a presumed 100% ratio was based. The result was a relatively lower ratio for a 1970 revaluing district (with Director's ratio over 100) than for the districts accorded the weighted ratios; a consequent inflation of such revaluing district's equalized valuations in relation to those of the others; and allocation *216 of an unfair share of the county tax burden to any such revaluing district. It could well have been argued, moreover, (a) that raising revalued districts' ratios to 100 automatically notwithstanding their ratios under the Director's tables were under that figure gave those districts a relatively unfair advantage as against all those districts (whether revalued or not) whose Director's ratios were used in the county equalization, and (b) that reducing the non-revalued districts with weighted ratios over 100 to 100 unfairly discriminated against them in relation both to all districts allowed to retain their weighted ratios as well as to those lifted to 100 from their weighted ratios.
Willingboro asked the Division to fix its 1970 equalization ratio at either the Director's final average ratio of 120.39 or his weighted ratio of 107.32.[9] For reasons later to be stated neither figure can be accepted; there must be a new equalization hearing and table by the Division of Tax Appeals.
The basic attack by Willingboro on the County board action is soundly grounded. Inspection of the Director's directive to the county boards and taxing districts dated September 30, 1969 which explains how the school aid tables of October 1, 1969 were constructed, reveals the following. The sales used *217 for calculating the Director's ratios (as to non-revalued districts) were (1) all those from July 3, 1968 to June 30, 1969 and (2) "all transactions used in the preparation of the [Director's] 1968 Table of Equalized valuations * * *." We have been advised that the period intended by the last phrase, and in fact applied, was that from July 1, 1967 to December 30, 1967.[10] It is thus apparent that for purposes of the Director's tables of October 1, 1969, calculation of ratios was based on sales going back to July 1, 1967. In view of the conceded continuously rising trend of realty market values thereafter it is plain beyond debate that the Director's October 1, 1969 ratios were founded upon data substantially earlier, and therefore materially lower than such indicia of value (whether sales or other valuation data) as would normally be used in revaluing a district for 1970 assessment purposes, the statutory valuation date therefor being October 1, 1969. N.J.S.A. 54:4-23.
The essence of the foregoing observations is also encompassed by the unrefuted testimony of Mr. Skelly, assessor of Willingboro, adduced before the Division of Tax Appeals.
Despite the foregoing, the Division found the county board's action correct because Willingboro had failed to prove that the "ratio of assessed value" assigned to it (100) was "below its true value" and because the board had treated the revalued districts in an identical manner. The Appellate Division affirmed the Division of Tax Appeals, saying in an unreported opinion:
"Although it might have elected to do so, the County Board was neither required to apply the 1970 [meaning October 1, 1969] table *218 of school ratios, nor was it precluded from placing a ceiling of 100% true value on the municipal equalization.
We are not convinced that plaintiff has carried the burden of proving that the Division or the Board acted arbitrarily or unreasonably. See Little Falls Tp. v. Passaic Co. Bd. of Taxation, 115 N.J. Super. 115 (App. Div. 1971), which involves substantially the same questions presented in this case and which appears to be controlling."
In the Little Falls case cited in the foregoing excerpt the Passaic County Board of Taxation had also fixed the 1970 equalization ratios at 100 for revalued districts notwithstanding the Director's ratios for them were higher, while setting the ratios for all other districts in accordance with those determined in the Director's school aid equalization table of October 1, 1969. The court noted that the complaining revalued districts admitted that they had assessed for 1970 at full true value and that the Director's tables had "been approved by our courts as an equalization measure" (115 N.J. Super. at 121), and it concluded (Ibid.):
"* * * Petitioners have merely shown that the county board utilized different methods and sources of determining the aggregate true values for the taxing districts of Passaic County. This the board was free to do, for all that was required of it was to carry out the equalization function in a reasonable and efficient manner."
The county boards, the Division of Tax Appeals and the Appellate Division in both the present and the Little Falls case fell into error. The cardinal principle which county boards of taxation must follow in the county equalization process was reflected in this expression of Justice Brennan in the leading case in this field, City of Passaic v. Passaic County Bd. of Taxation, supra (18 N.J. at 390):
"When a county board increases an aggregate submitted by a local assessor, not `from any judgment formed by them that the valuation * * * was relatively less than it should have been,' State, Weehawken Twp., Pros., v. Roe, supra, 36 N.J.L., at page 89, but from considerations foreign to the relation of the average assessment ratio reflected therein to the average assessment ratios of the aggregates of the other taxing districts, the action is, in law, arbitrary and oppressive and the table must be set aside." (Emphasis added.)
*219 The mandate for accomplishment of relative equalization as among the taxing districts was not here followed by the county board or the Division. It was of no materiality, alone, that Willingboro and other reassessing districts had purported to set 1970 assessments at relatively current true value if no effort was made by the Board or the Division to ascertain whether the Director's weighted ratios for the districts given such ratios by the board were based upon valuation data substantially similar in quality to those which were the foundation of the assessments of the revalued districts; and, if not, to settle upon and apply substantially similar data and a common standard uniformly in determining ratios of assessments to true value for all districts in the county. The substantial dissimilarity of the underlying data and standards in the respective categories of districts is here quite obvious. The fact that nominally the standard was the same percentage of true value for both sets of districts cannot hide the crucial fact that actually a differently constructed standard of "true value" was applied to each group, operating discriminatorily against the revalued districts with Director's ratios over 100 (and equally discriminatorily in favor of revalued districts with Director's ratios under 100).
Thus, the evidence before the Division should have put it on notice of substantial prima facie disparities between the relative standards applied by the county board in fixing the ratios for any revalued district as opposed to any non-revalued district and as between districts of either category where there were either arbitrary increases of weighted ratios to 100 or reductions of such ratios to that figure. Upon these showings, it became the duty of the Division to prepare a proper equalization table, and for that purpose to conduct a de novo equalization hearing, on notice to all districts, itself seeking out, if necessary, any pertinent and relevant data, and proceeding in the manner enjoined by the statute upon the county boards for fixing the final equalization table. City of Passaic, supra (18 N.J. at 395); Woodbridge v. *220 Middlesex Co. Bd. of Taxation, et al., 96 N.J. Super. 532, 536 (App. Div. 1967).
We pointed out above (in note 9, supra) that there was an additional special problem applicable to Willingboro as a district which had reassessed in the tax years 1968 and 1969 as well as 1970. Because of the reassessment in 1969 a special provision of the Director's directive for preparation of the October 1, 1969 school aid tables became implicated in relation to calculating the ratios for Willingboro. This was that the sales sampling period applicable to 1969  reassessed or revalued districts was specified as only from January 1, 1969 to June 30, 1969, as contrasted with the longer and earlier period used in respect of the other districts. We are satisfied, however, that by reason of the "double-averaging" of the 1969 equalized valuations of the revalued districts with those of 1968, as explained in note 9 above, the effect of the disparate sales sampling periods has been sufficiently neutralized as a practical matter in this particular regard.
We recognize the correctness in principle of the argument urged upon us on behalf of the county board that any reasonable and efficient method of equalization may be used; that mathematical exactitude is not required; and that a degree of imperfection will be tolerated. Woodbridge v. Middlesex Co. Bd. of Taxation, et al., supra (96 N.J. Super. at 536), holding that a board may use an unweighted instead of a weighted method of sales ratio analysis if applied uniformly to "all of the taxing districts in the county" (emphasis in the original) (Id., at 538). Moreover, the equalization process cannot as a practical matter be encrusted with "rigid technicality and formalism," Kearny v. Div. of Tax Appeals, 35 N.J. 299, 311 (1961). Yet the overriding legislative purpose is the equal, proportionate sharing of the county tax burden, and when a method  any method  used imposes on a particular municipality a share "dramatically or substantally excessive" the review agency or the court must grant relief. Id., at 310.
*221 As already shown, the separate decisions of the county board concerning ratios to be assigned revalued districts on the one hand, and non-revalued districts on the other, cannot be adjudged for correctness independent of each other, as assumed by the tribunals below. This also applies to the artificial bench-mark of the county board precluding a ratio over 100 for any district. The crucial issue concerns the interrelated effect of each of these decisions on the proportionate county tax burden of all the districts. The failure to apply a common standard to each district necessarily distorted the burden-sharing balance of all.
For the reasons stated there is a prima facie basis to believe that some municipalities in Burlington County were necessarily subjected to excessive proportionate shares of the county tax burden for 1970 in favor of others by the methods and principles here used. The degree of excessiveness cannot be estimated on this record, nor is it material, for present purposes. The Division must reexamine the matter. We proceed to a consideration of possible alternative methods of equalization, for the guidance of the Division.

III. Remedies

The major problem calling for practical solution is how to treat revalued districts, where the county board desires to avail itself of the Director's school aid ratios and equalized true valuations as to the others, and yet remain consistent with the objective of distribution of the county tax burden on the statutory basis of the relative proportion to the whole, of the aggregate true value of the ratables in each district. We have already explained why the Director's ratios, whether weighted or final average, cannot without resulting disproportion be directly applied to the assessments of a revalued district. The Director has since 1957 been recommending to county boards of taxation what is *222 commonly called the page 8 formula[11] for the practical handling of the problem on a theoretically fair basis.
The formula was designed by the Division of Taxation to produce equalized valuations in the new tax year for revalued districts which will correspond in method of determination with the equalized valuations for non-revalued districts resulting from use of the Director's ratios as applied to such districts in the ordinary course by county boards in the manner already described.
Before describing it in detail, we point out that the formula is essentially but a different method of deployment of the identical data in the Director's table pertaining to both categories of district which, in principle, produces a harmonious county equalization as between revaluing and non-revaluing districts. Putting aside, for the moment, its provision for adjustment of the Director's equalized valuations in respect of added and omitted assessments, new construction, etc., in revalued districts, the formula, in principle, simply seeks to avoid the disproportionate effect in revalued districts, noted above, of dividing the new assessments by the Director's ratio. It does this by dividing the aggregate new assessments of the revalued district by the Director's equalized true valuations therefor, thereby producing a wholly new ratio, which, when divided into the aggregate new assessments, yields a county equalization true value aggregate for the district which in fact accords, proportionately, with the county equalization true value aggregates for the non-revalued districts resulting from the normal division of the new year's assessments in such districts by the Director's ratio therefor.
The formula is essentially as follows.[12]
*223 Item A is the aggregate of the assessor's revalued assessments for the new tax year. It becomes the dividend which upon division produces the entirely new ratio, mentioned above, to be used in the revalued district. The divisor in that division computation is Item B, which is constructed in this manner: (a) set forth the aggregate equalized true valuations for 1969 certified in the Director's October 1, 1969 table; (b) add thereto the aggregate added and omitted property assessments, as set forth in the lists as of October 1, 1969 (pursuant to N.J.S.A. 54:4-63.2 et seq. and N.J.S.A. 54:4-63.12 et seq.), equalized to true value by the Director's October 1, 1969 ratio; (c) add thereto the aggregate ratables of new construction, improvements, exempt property transferred to taxable, all equalized by the ratio "claimed" to be used in 1970 by the assessor; (d) deduct from the total of (a), (b) and (c) the sum of losses in ratables from fire, demolition and transfer of taxable property to exempt, equalized to true value by the Director's October 1, 1969 ratio. The resulting remainder is Item B, putatively the aggregate true value of the district on December 31, 1969 and January 1, 1970. Division of Item A by Item B produces the ratio which, as noted above, the Director recommends the county boards divide into Item A to produce the 1970 equalized true valuations in the revalued districts.[13]
*224 A preliminary comment is in order. The basic figure in the page 8 formula is Item B(a) above  the certified equalized true value in the Director's October 1, 1969 table  and that figure is the result of averaging the 1969 true valuations (corresponding to the weighted ratio) and the certified equalized 1968 true valuations, the resulting average being the certified equalized 1969 true valuations (corresponding to the final average ratio). Accordingly, if the page 8 formula were to be applied literally in 1970 for county equalization purposes, the county boards would for consistency have to assign to all non-revalued districts the Director's final average ratios rather than the weighted ratios, as was here done by the county board. This is more than a technicality since the certified average equalized valuations were substantially lower than those equalized for 1969 alone, being depressed by the lower valuation data entering into the certified 1968 true valuations. Or, as an alternative, the county board could retain the weighted ratios for the non-revalued districts if it modified the page 8 formula by substituting for Item B(a) as specified the equalized true valuations for 1969 alone (before averaging).[14] Notwithstanding we appreciate the Director's overall purpose in averaging to achieve a slower rate of change in ratios, either up or down, it might still be preferable to apply the weighted ratios in order to maintain the county equalized valuations at a scale closer to the values as of the assessing date for the particular tax year (here 1970). However we dictate no choice.
The argument advanced for use of the page 8 formula by the Deputy Attorney General whom we asked to brief it for the reargument of the appeal is persuasive. It is based on the principle of use of underlying sales data of the same quality in equalization of assessed ratables for both revalued *225 and non-revalued districts. The courts have adverted to its use without criticism of it, e.g., In re Township of Millburn, 110 N.J. Super. 330, 335 (App. Div. 1970); Bor. of Wood-Ridge v. Bergen Co. Bd. of Tax., 111 N.J. Super. 174, 178 (App. Div. 1970). We are told that the formula has been used by 15 of the 21 county boards of taxation.
Moreover, the slight aberration in effect for 1969-70 mentioned in note 9 and found by us above not to involve any serious disproportion as against districts revaluing in the year of the Director's table has been futher ameliorated by changes in the method of formulating the Director's tables in 1970 and thereafter. The directive for 1970 sharply curtails the length of the general sales sampling period, confining it to the dates July 1, 1969 through June 30, 1970. The sales study period for districts revaluing for 1970 is from January 1, 1970 through June 30, 1970. This minor degree of difference in the respective sales periods used may well conduce to a conclusion that it is so slight in effect that the resulting ratios (coupled with use of the page 8 formula as to districts revaluing in 1971) can be applied for 1971 county equalization purposes within the bounds of reasonable fairness.[15] However, we do not now decide any issue as to 1971 county equalization.
We should emphasize, if it is not already clear, that there is nothing anomalous in some districts being accorded ratios of over 100 and others less in a county equalization table. The statutory mandate of individual assessment at 100% of true value in Burlington County (by county board resolution) has no relationship to the proper fixing of ratios for county equalization purposes as between taxing districts. Because of the subjective element in assessing, and the customary use by county boards of the Director's ratios, it is inevitable that the ratios of actual aggregate assessments to true value will vary above and below *226 100% depending not only upon the accuracy of judgment and good faith of the assessors but also upon a comparison between the date as of which assessment valuations are determined and the time period for sales used by the Director in computing the ratios. A county board should therefore never reject a municipal ratio arising from a sales study by the Director for no better reason than that it exceeds 100.
At the reargument amicus curiae, Mrs. Yahnel, who is tax analyst for the Middlesex County Board of Taxation, objected to the page 8 formula on the ground, as we understand it, that in effect it employs as a base for equalized valuations, even though uniformly, valuation scales too remote in time from the taxing date for the current county equalization year. This, she argues, ignores the incidence of variations between taxing districts, as of the current tax year assessing date, as to such spurs to accelerated general increases in value in particular districts as recent land subdivisions and other kinds of land development tending to increase surrounding values, not reflected in the sales studies as of an earlier time period producing the Director's ratios.
A partial answer is that the page 8 formula requires adding to the Director's equalized valuations for revalued districts the added assessments and new construction, equalized, as of October 1 of the Director's equalization year, which is the same date as the assessing date for the county equalization tax year; and, correlatively, that the assessed valuations for the non-revalued districts presumably pick up newly completed improvements as of said same preceding October 1.
However, the more pointed response to the argument is that considerations of practical administrative feasibility must control over those of a theoretically perfect plan. See Bayonne v. Division of Tax Appeals, supra (49 N.J. Super., 237-240). The availability of the Director's tables gives the county boards a valuable working tool which, by and large, they do not have the facilities and manpower to develop themselves. Since the Director's tables must be formulated *227 by October 1, and must necessarily rely on sales analyses for time periods of reasonable length, yet ending early enough to leave adequate time for workup of the tables statewide by October 1, some gap between the mean valuation date reflected by the Director's sales analysis period and the legal assessing date for the new tax year is inevitable. We do not regard such a gap as sufficient to impair the Director's tables as a proper foundation for the data used in the following years' county equalization, despite the point made by the amicus, since equalization is an intensely practical operation, need not be perfect, and is adequate and lawful if fair over the long run and substantially free from disparity of method as betweeen taxing districts. We hold use of the page 8 formula would meet those criteria in this particular case (subject to the caveat noted above, as to use of parallel ratios).
While we thus approve and encourage the use of the page 8 formula on the remand by the Division of Tax Appeals, subject to any legitimate new objection which may be raised by any taxing district not a party to this appeal which must under the statute be heard at the new hearing, we are unable at this time to say it is the only tenable approach. It is settled that no particular method of equalization is mandatory for a county board of taxation. "* * * [A]ny reasonable and efficient mode may be adopted." City of Passaic, supra (18 N.J. at 385). A number of the boards, including Middlesex County's, use different methods in handling the problem of revalued districts. Some apparently use methods of equalization (without regard to the problem of revalued districts) somewhat different from those of the Director, although practically all develop sales ratio studies of some kind, and we cannot say that any of them are invalid outside the context of the record of a particular case. We therefore do not accept the suggestion of the Director of the Division of Taxation that we order all county boards hereafter to use the page 8 formula for revalued districts *228 where they use the Director's ratios for non-revalued districts, although we encourage it.
We cannot accede to Willingboro's request that it be summarily accorded either the Director's 1969 final average ratio of 120.39 or his weighted ratio of 107.32. Since the ratio of any district mathematically affects the dollar share of county tax burden of every other, and a proper ratio for each can emerge only after a correct determination of the relative equalized valuations of all, a final assignment of ratios must await a redetermination of the whole table after a new hearing by the Division of Tax Appeals consistent with the principles discussed in this opinion in relation to the particular considerations involved and after taking account of any additional pertinent proofs offered.
A final consideration suggests itself. A new and correct equalization table for 1970 will effect a reallocation of the respective shares in the 1970 cost of county government of each municipality. It may be that the immediate financial effect of the reallocation on particular municipalities will be oppressive if required to be met at one time. If so, on application to the Division within 20 days after notice of its redetermination, that body may direct appropriate reimbursement as between municipalities in such annual installments or otherwise as may seem just. Cf. Vail Mut. Assoc. v. Speaker of House, 107 N.J. Super. 517; 533-534 (App. Div. 1969), aff'd sub nom. Alfred Vail Mut. Assoc. v. Bor. of Shrewsbury, 58 N.J. 40, 54 (1971).
Reversed and remanded to the Division of Tax Appeals for a new hearing and determination of the Burlington County tax equalization table for 1970 consistent with this opinion. No costs.
For reversal and remandment  Chief Justice WEINTRAUB, Justices JACOBS, HALL and MOUNTAIN, and Judges CONFORD and LEWIS  6.
For affirmance  None.
NOTES
[*]  It appeared at the original argument that methods of dealing with reassessed taxing districts for county tax equalization purposes, different from that of the Burlington County Board of Taxation defended by the deputy attorney general appearing, were being used by various other county boards of taxation. The court therefore requested that the merits of the so-called page 8 formula (described infra), used by some 15 county boards, be briefed and argued by Mr. Saxe, and that the method used by the Middlesex County board be presented by its tax analyst, Mrs. Yahnel. The latter appears to represent a sui generis approach which we do not find it necessary to discuss in order to decide this case. We imply no opinion concerning its merit.
[1]  Certain portions of the factual material set forth in this opinion are based upon information supplied the court at its request by the Director of the Division of Taxation of the State Department of the Treasury subsequent to the reargument. This has been on notice to all parties, and there has been no factual dispute as to any of such material.
[2]  Leading to legislative direction for assessment at fixed percentages of true value, to be set by county boards of taxation. L. 1960, c. 51.
[3]  The greater the equalized valuations, the less (in general) the state aid.
[4]  There are two Director's 1969 ratios, the "weighted ratio" and the "final average ratio". The difference is discussed hereinafter.
[5]  The problem also confronted the Passaic County Board of Taxation in 1970. As noted above, it was dealt with in the same fashion as the Burlington board did here. See Tp. of Little Falls v. Passaic County Bd. of Tax., supra, discussed fully hereinafter.
[6]  E g., in relation to the Director's table of October 1, 1969, the numerator of the fraction which produces the ratio is constituted by the aggregate of the assessments for the tax year 1969 (although individual assessments for 1969 are made as of the valuation date October 1, 1968).
[7]  It is to be noted that the amount or changes in the amount of equalized true valuations for any district automatically affect the shares of county government cost of all others since each contributes in the proportion of its own equalized true valuations to the county total. In contrast, the amount of equalized true valuations of a school district under the Director's tables does not affect the allocation of school aid of any other district.
[8]  We use the terms "reassessment" and "revaluation" interchangeably, as they are also used throughout the record. Generally, "revaluation" is the term used when conducted by an outside professional agency; "reassessment", when done by the assessor. The state local property tax burau classifies as revalued or reassessed districts those where over 80% of the assessment items have been significantly changed in one year.
[9]  The Director arrived at his 1969 ratios for Willingboro in a manner different from that ordinarily used. This is because Willingboro revalued for 1969 as well as for 1970. For 1969-revalued districts, the Director used only sales occurring between January 1, 1969 and June 30, 1969, a much shorter and relatively later period, as seen above, than used for establishing the ratios of non-revalued districts. While this circumstance might at first blush seem to involve disproportionate bases for the respective categories of districts, to the detriment of the 1969-revalued districts, that consequence was avoided by the Director through the technique of a preliminary averaging of the 1969 equalized valuations of the re-valued districts with those of the 1968 table prior to the averaging of the resulting equalizations of all the districts with those of 1968. In other words, the revalued districts were accorded a "double-averaging" with the lower 1968 equalized valuations to compensate for the difference in the respective sales periods.
[10]  Sales from January 1, 1968 to June 30, 1968, which would normally have been included in the analyses leading to the October 1, 1968 tables, were excluded because reliable information in respect thereof was unavailable due to the expiration on December 31, 1967 of the operation of the Federal Documentary Stamp Tax Act. (Sales prices after July 3, 1968 were obtained from recordings complying with the New Jersy Realty Transfer Fee Act, N.J.S.A. 46:15-5 et seq.)
[11]  The term derives from the numbered page of a memorandum of the Division of Taxation dealing with the problem of revalued districts and county equalization on which the formula itself is set forth.
[12]  The description of the formula which follows is, for purposes of clarity, set out in terms of the use of the Director's table of October 1, 1969 for application to a county equalization table for 1970.
[13]  The purpose of the adjustments in Item B(b), (c) and (d) is to compensate for the fact that such items are presumably reflected in the assessed valuations for the next tax year of all the districts.

It will be observed that the last step in the process just noted as to a revalued district is in theory unnecessary since it in effect constitutes the already determined Director's equalized valuations (as modified by the adjustments provided for) as the county board equalized valuations of the district for the current tax year. However that step is formally indicated since the statute requires the ratio to be stated in the county equalization table (N.J.S.A. 54:3-17) and in theory contemplates that the equalized valuations will result from it, as they in fact do in the case of non-revalued districts.
[14]  That would also, in that case, entail the use of the Director's weighted ratio rather than the final average ratio in relation to Items B(b) and (d) of the page 8 formula, as set forth above.
[15]  The Director's directives for 1971 and 1972 follow that of 1970.
