
178 N.W.2d 759 (1970)
185 Neb. 749
In the Matter of the Valuation and Equalization of Real Estate in Gage County, Nebraska for 1969.
GAGE COUNTY, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
In re Matter of the Valuation and Equalization of Adams County, Nebraska for 1969.
ADAMS COUNTY, Nebraska, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
In re Matter of Valuation and Equalization of Real Estate in Phelps County, Nebraska for 1969.
PHELPS COUNTY, Nebraska, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
BUFFALO COUNTY, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
In the Matter of the Valuation and Equalization of Real Estate in Clay County, Nebraska for 1969.
CLAY COUNTY, Nebraska, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
In the Matter of the Valuation and Equalization of Saline County, Nebraska for 1969.
SALINE COUNTY, Nebraska, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
In the Matter of the Valuation and Equalization of Jefferson County, Nebraska for 1969.
JEFFERSON COUNTY, Nebraska, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
In the Matter of the Valuation and Equalization of Hitchcock County, Nebraska for 1969.
HITCHCOCK COUNTY, Nebraska, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
Nos. 37399, 37401-37406 and 37411.
Supreme Court of Nebraska.
July 17, 1970.
*761 K. E. Mahlin, County Atty., Beatrice, McGrath, North, Nelson, Shkolnick & Dwyer, Omaha, for appellant Gage County.
William M. Connolly, County Atty., Hastings, McGrath, North, Nelson, Shkolnick & Dwyer, Omaha, for appellant Adams County.
J. Clark Noble, County Atty., Holdrege, McGrath, North, Nelson, Shkolnick & Dwyer, Omaha, for appellant Phelps County.
Andrew J. McMullen, County Atty., Kearney, McGrath, North, Nelson, Shkolnich & Dwyer, Omaha, for appellant Buffalo County.
Jay J. Sullivan, County Atty., Clay Center, McGrath, North, Nelson, Shkolnick & Dwyer, Omaha, for appellant Clay County.
Bernard J. Ach, County Atty., Friend, McGrath, North, Nelson, Shkolnick & Dwyer, Omaha, for appellant Saline County.
Robert F. Lammers, County Atty., Joseph F. Chilen, Fairbury, McGrath, North, Nelson, Shkolnick & Dwyer, Omaha, for appellant Jefferson County.
Robert C. Bosley, County Atty., Hayes Center, McGrath, North, Nelson, Shkolnick & Dwyer, Omaha, for appellant Hitchcock County.
Clarence A. H. Meyer, Atty. Gen., Ralph H. Gillan, Asst. Atty. Gen., Lincoln, for appellee.
Heard before SPENCER, BOSLAUGH, SMITH, McCOWN, and NEWTON, JJ., and COLWELL and TESAR, District Judges.
McCOWN, Justice.
This case involves the appeals of eight counties of the State of Nebraska from orders entered by the State Board of Equalization and Assessment increasing the 1969 assessed value of real estate in the respective counties for property tax purposes. The cases were consolidated for briefing and argument. The basic questions involved are whether or not a constitutionally uniform standard of valuation was used; whether that standard was uniformly applied; and whether or not the appellant counties were properly equalized in relationship to each other and to other counties within the state.
At the outset, we think some general observations are appropriate. The taxes involved are ad valorem taxes on real property, levied and assessed by local governmental units. The state itself may not levy such taxes for state purposes. The Constitution requires that such a property tax be "* * * levied by valuation uniformly and proportionately upon all tangible property * * *." Examination of the record discloses extensive divergence among witnesses of all categories in their understanding of the meaning of uniform values in the constitutional tax context. Many witnesses seem to assume that real property taxes may be equalized if property is classified, and the same values applied to the same classifications of property in all counties. The Constitution itself flatly contradicts such a conclusion. Art. VIII, s. 1, Constitution of Nebraska.
The Legislature has attempted to define "actual value" for purposes of taxation by application of a formula "where applicable." S. 77-112, R.R.S.1943. While the items of the formula are all related to *762 value, those which are factors in determining value are by no means the only factors which enter into the valuation of property for taxation. As this court said in Richards v. Board of Equalization, 178 Neb. 537, 134 N.W.2d 56: "For purposes of taxation, the terms actual value, market value, and fair market value mean exactly the same thing. Many elements enter into a determination of actual value, some of which are set out in the statute."
We suspect that the legislative attempt to define value for purposes of taxation has distorted the relationships of many elements of value, and has intermixed methods of measuring value with elements and factors entering into any proper determination of value. The term "fair market value," while it is an intangible concept, has had a definite and well understood legal meaning over a very long period of years. The attempt to define that concept of value as being readily ascertainable by means of a formula "where applicable," has added to the misunderstanding.
We should note also that so far as we are able to determine, Nebraska is the only state which provides by statute that equalization of the assessment of real property shall be done by each local county board of equalization; then by a state board as to all counties; and that in the event of disagreement between them, the matter may be settled by litigation between the two in this court. To say the least, it is a somewhat unusual procedure. The determination of both county and state boards of equalization is clothed with a presumption of validity. Nevertheless, as a practical matter, the problem has been further complicated by the fact that the state board, by statute, is subject to the requirements of the Administrative Procedures Act. See S. 84-901, R.R.S.1943. The county board of equalization is not. It has, therefore, been necessary for this court to require and hold that the record of the proceedings before the state board must be sufficient to sustain the action taken by that board. See, Hanna v. State Board of Equalization & Assessment, 181 Neb. 725, 150 N.W.2d 878; City of Omaha v. State Board of Equalization & Assessment, 181 Neb. 734, 150 N.W.2d 888.
We proceed with a consideration of the facts relative to the appeal of Gage County separately from the remaining counties since its treatment was distinct. Gage County had a statutory scientific reappraisal of its real property which was completed in 1968 and approved by the State Tax Commissioner as provided by statute. Gage County rolled back the valuations set by the scientific appraisal by 20 percent and placed the appraisal in effect for the first time in 1969 at the reduced valuations. The order of the state board simply restored the reappraisal values for Gage County to their original level.
The record is clear that all scientific reappraisals conducted in accordance with the statute and approved by the State Tax Commissioner, completed and placed in effect within two or three years prior to 1969, were accepted and approved as filed by the state board. Approximately 30 such appraisals were accepted and approved without change by the state board. The use of such scientific appraisals has long been approved and, in fact, is the traditional method of valuation in this state. The action of the state board was consistent with its procedure in connection with all such appraisals. There is likewise no contention on the part of Gage County that the original full appraisal values exceeded actual value. We think it clear that where the evidence discloses the consistent use of reasonably current reappraisals, done under uniform conditions and regulations and approved by the State Tax Commissioner, such procedures meet the constitutional test of uniformity. We, therefore, approve the order of the state board as applied to Gage County.
*763 The following statistical information sets out the relevant findings and orders of the state board, with respect to the remaining seven counties involved here.


                                                      Urban and Suburban
                    Agricultural Land                      Property
              Assessment         Assessment      Assessment       Assessment
  County      Sales Ratio         Increase       Sales Ratio       Increase
                                   Percent                          Percent
                                   ordered                           ordered
  Adams          20                  75              28                20
  Buffalo        20                  75              28                10
  Clay           22                  59              28                15
  Hitchcock      25                  40              28                0
  Jefferson      25                  40              30                15
  Phelps         20                  75              29                15
  Saline         25                  40              28                15

It should be noted here that the assessment sales ratios shown above are the specific findings of the state board as to these counties. Five of the counties had assessment sales figures for each of the three preceding years. One county had two-year figures, and one had only the last year. Where there were assessment sales figures for three years, however, the state board followed no consistent procedure in making its findings. In some instances, perhaps most, the board used an average of the three years assessment sales figures. In some, it was the latest year (1968). In one or two others, it was neither an average nor the last year.
In some instances, the treatment was different in the same county between agricultural and urban property. For example, in Saline County, the assessment sales ratio figure for agricultural land in 1968 was 25. The figure for 1967 was 26, and for 1966 was 28. The average was 26.3, but the 1968 figure of 25 was used. For urban property in Saline County, the 1968 assessment sales ratio figure was 27, the 1967 figure was 30, and the 1966 figure was 29. The average was 28.6, and 28 was the finding.
In Jefferson County, an average of the assessment sales ratios for three years was used to find the agricultural assessment sales ratio, while only 1968 was used to determine the urban assessment sales ratio, although the two preceding years were each higher.
In each instance, the order of the state board as to the counties involved here, except Gage County, shows that the assessment increases ordered, at least as to all urban and suburban property, were based upon the assessment sales ratios and "testimony of county officials." The testimony of county officials directly opposed any increases by the state board except in the case of agricultural land in Hitchcock County. It is quite apparent that the ordered increases in the seven counties stem directly from the assessment sales ratio figures determined by the state board. With respect to agricultural land, the increases ordered in each instance fit the assessment sales ratio figures exactly. With respect to urban and suburban property, however, it is equally apparent that the assessment sales ratio figures were not followed. It will be noted that the state board findings show that five of the seven counties had assessment sales ratios of 28 for urban and suburban property. The state board increased the assessment of one of the five counties by 20 percent; two by 15 percent; one by 10 percent; and one *764 nothing. There is no evidence in the record which will explain or support that disparity in treatment.
In 1966, this court held that the state board may adopt any reasonable method of equalization, including the use of reasonably reliable assessment sales ratios. County of Lancaster v. State Board of Equalization & Assessment, 180 Neb. 497, 143 N.W.2d 885.
Later, we reversed state board action where "the record does not reveal the basis of correlation, or the basis of application, of the methods used for measuring and testing uniformity." See City of Omaha v. State Board of Equalization & Assessment, 181 Neb. 734, 150 N.W.2d 888.
The object of constitutionally required uniformity in the taxation of real property is accomplished if all of the property within the taxing jurisdiction is assessed and taxed at a uniform standard of value. See Carpenter v. State Board of Equalization & Assessment, 178 Neb. 611, 134 N.W.2d 272.
It is apparent from the record here that the state board has applied assessment sales ratios on the one hand, and recent reappraisals approved by the State Tax Commissioner on the other, as precisely equal methods of measuring and applying uniform values. Yet the record itself overwhelmingly demonstrates that these two methods, as presently applied, do not produce an equal or uniform level of value. In the 1969 year involved here, approximately 30 counties had used reappraisals, approved by the State Tax Commissioner, which were accepted without change by the state board. Of those counties, 19 of them also had assessment sales ratio figures for the same year in which the appraisal first went into effect. This represents 20 percent of the counties in this state. Mean and average figures coincide. For agricultural land, these statistics for 19 counties show an average difference of more than 25 percent in the values reflected by recent approved appraisals and values reflected by assessment sales ratios in the same county and for the same year. Such differences are in no way correlated by the state board, and either or both methods have been used as though they each reflected exactly the same level of value. The evidence contradicts that assumption. Necessary correlation could have been made, but it would not have supported the percentages of increase ordered in these cases.
The difference between the values reflected by the two methods when applied to urban and suburban property is much less. Both mean and average differences here approximate 12 percent. While such differences might be within reasonable practical limits if they had been applied consistently by the state board, it is apparent that this was not done as to the seven counties involved here. The percentage increases in urban property ordered by the board in five of the counties involved here varied from 0 to 20 percent, yet they were based on identical assessment sales ratios. We find nothing in the record to justify this lack of uniformity.
Where the record on appeal from an order of the state board establishes an arbitrary adjustment, the order must be reversed. See County of Keith v. State Board of Equalization & Assessment, 180 Neb. 494, 143 N.W.2d 902. The record here with respect to the seven counties under consideration fails to support the orders entered. A uniform and proportionate standard of value was not used or applied to all counties alike. The constitutionally required equality or uniformity cannot be achieved except in relationship to a uniform standard of value.
In dealing with the intangible concepts of valuation and uniformity, a mathematically precise result can never be achieved. Neither mathematical exactness nor precise uniformity is possible in the complex task of equalization Nevertheless, the bounds of reasonable uniformity do not stretch to the scope given them *765 here by the state board. This court cannot act as a super-board of equalization, nor substitute its judgment for that of the state board. We cannot escape the conclusion that constitutional and statutory requirements were not met as to the seven counties involved here. The state board still has the opportunity to rectify the situation.
The order of the State Board of Equalization and Assessment as to Gage County real property is affirmed. The orders of the State Board of Equalization and Assessment as to the remaining counties herein are reversed.
Affirmed in part, and in part reversed.
WHITE, C.J., and CARTER, J., took no part in the consideration of or decision in these cases.
