
549 N.W.2d 164 (1996)
250 Neb. 323
HALL COUNTY, Nebraska, Appellant,
v.
STATE BOARD OF EQUALIZATION AND ASSESSMENT, Appellee.
No. S-95-895.
Supreme Court of Nebraska.
June 14, 1996.
*166 Jerom E. Janulewicz, Deputy Hall County Attorney, for appellant.
Don Stenberg, Attorney General, and L. Jay Bartel, Lincoln, for appellee.
WHITE, C.J., and CAPORALE, FAHRNBRUCH, LANPHIER, WRIGHT, CONNOLLY, and GERRARD, JJ.
WHITE, Chief Justice.
This is an appeal by Hall County, Nebraska, from the order of the State Board of Equalization and Assessment (board), dated August 15, 1995, refusing to order a reduction in the assessed valuations of taxable real property in Hall County.
*167 Hall County contends that by refusing to reduce the assessed residential real property values in Hall County, the board acted arbitrarily, capriciously, and contrary to law, and its action constitutes an abuse of discretion. Because we find that Hall County failed to meet its burden in proving that the board acted arbitrarily and capriciously, we affirm.
On July 14, 1994, the board established the standards to be used for the equalization of real property values for 1995. The board adopted a motion setting outside limits of the assessed values at 92 percent and 100 percent for residential and commercial/industrial property, and 74 percent and 80 percent for agricultural property. The board ordered counties that assessed their property outside of these limits to show cause why their assessed values should not be adjusted to conform to its decision.
Based on the board's motion, county assessors and county boards of equalization set values of locally assessed real property on or prior to June 15, 1995, as required by Neb.Rev.Stat. § 77-1506.02 (Cum.Supp. 1994).
The board met on July 14, 1995. After reviewing the assessed values for all of the counties in the state, the board determined that 13 counties had assessed values of residential property lower than 92 percent. Of these counties below the 92 percent floor that was set by the board in 1994, five counties were located in the same community college taxing district as Hall County. These counties included (1) Adams County, with an assessed residential value of 91 percent; (2) Clay County, with an assessed residential value of 90 percent; (3) Kearney County, with an assessed residential value of 89 percent; (4) Platte County, with an assessed residential value of 91 percent; and (5) Boone County, with an assessed residential value of 89 percent.
At this July 14 meeting, the board adopted a new policy which reduced the minimum acceptable assessed values to 89 percent for residential and commercial/industrial property and to 71 percent for agricultural property. The board also decided to issue a notice to show cause, requiring a county to show cause why adjustments for property values should be made in order to achieve a just, equitable, legal assessment of real property in the state.
Following the board's action on July 14, Hall County filed a petition for reduction of valuations. The petition stated that taxable real property for the tax year 1995 had been assessed by Hall County at the following percentages of fair market value: residential, 98 percent; commercial/industrial, 100 percent; and agricultural land, 74 percent.
Hall County's petition further alleged:
As a result of the July 14, 1995, action of the State Board, classes of real property, particularly residential property, in various counties, including Douglas, Adams, Boone, Clay, Dodge, Kearney, Madison, Platte, Saunders and Washington, will be valued for tax purposes at a lesser percentage of fair market value than property within the same classes within Hall County. Adams, Boone, Clay, Kearney and Platte counties are within the same community college district as Hall County and, as a result of the disproportionate valuations within said district, property with[in] Hall County will be taxed at a proportionately higher rate than will property located in other counties within the community college district.
Hall County alleged that a reduction of residential property to 89 percent of fair market value and commercial/industrial property and a reduction of agricultural property to 71 percent of fair market value was necessary to achieve intercounty equalization.
On August 11, 1995, the board held hearings requiring Hall County, and 10 other counties that responded to the notices, to show cause why their assessed values should be reduced. At this hearing, the board heard testimony from five Hall County representatives. The representatives complained of the board's decision on July 14 to reduce the minimum parameter to 89 percent of fair market value. They also requested that residential property in Hall County be adjusted to the levels that were requested in Hall County's petition for reduction.
Hall County also submitted an affidavit of Janet Pelland, the Hall County assessor. *168 This affidavit listed various taxing districts that included Hall County. This list included the counties located in the community college district, the district that Hall County expressed concern about in its petition.
On August 14, the board held a meeting to determine if adjustments should be made with regard to the counties requesting reductions. The board discussed these counties according to their geographical location to determine how the requested assessed value adjustments correlated with neighboring counties.
The board first considered a motion to reduce the assessed value of Sarpy County from 94 percent to 89 percent of fair market value. Sarpy County presented extensive evidence indicating that a 94 percent assessed value created significant inequalities in taxation with bordering Douglas County, which had an assessed value of 89 percent. The board therefore adopted this motion so as to equalize Sarpy County's property values with those of Douglas County.
The board then addressed Rock and Keya Paha Counties' requests to create a more equalized assessment with the neighboring counties in the north central region of the state. The board adopted a motion to reduce the assessed residential property value of both of these counties to 91 percent. The board then discussed whether, by adopting this motion, a tax shift would occur resulting in agricultural landowners in these counties bearing a heavier tax burden. The board concluded that a tax shift to agricultural land would be insignificant because there was very little residential property located in these counties.
The board then addressed the counties located in the central portion of the state that were seeking reductions. The board first adopted a motion to reduce the assessed residential value of Dawson County by 6 percent, from an assessed value of 100 percent to 94 percent.
The board then considered a motion to reduce the assessed values of residential property in York, Hamilton, Frontier, and Hall Counties to an assessed value of 92 percent. Gary Quandt, a Hall County supervisor, was present at the board's discussion of this motion. He urged that Hall County should be reduced to 89 percent because of the lower assessed values of the surrounding counties that are in the same community college taxing district. He stated that a reduction to 92 percent was acceptable if that was the maximum reduction the board would consider.
The board ultimately adopted the motion to decrease the assessed value of residential property in Hall, York, Keya Paha, and Frontier Counties to 92 percent.
However, immediately after adopting the motion, the board again indicated a concern that such reductions in residential values could result in an unintended tax shift to agricultural land. The board therefore addressed the issue of whether it was necessary to make an appropriate adjustment to the assessed value of agricultural property so as to prevent a tax shift resulting in an undue tax burden on agricultural landowners. The board's primary concern was that a tax shift to agricultural land or a reduction in the assessed value of agricultural land would extend over county lines and create inequalization in taxing districts, imposing a heavier tax burden on agricultural landowners.
In addressing this issue, the board reviewed a document prepared by the property tax division of the Nebraska Department of Revenue. This document was a statistical table which separated the property of the 11 counties under consideration into subclasses, such as residential, commercial/industrial, and agricultural. The table broke down the total value of all property for each county into percentages according to subclass. The table also indicated how these subclass percentages would change if the assessed value of residential property were reduced a particular percentage.
With regard to Hall County, the table was based on a 4-percent reduction in the assessed valuation of residential property, rather than the 6-percent reduction adopted by the board. The table indicated that residential property consisted of 49.31 percent of total property value in Hall County. The table reflected that a 4-percent decrease in the assessed value of residential property *169 would decrease the percentage of the residential property value to 48.29 percent of total property value. With regard to the agricultural land, the table indicated that the percentage in Hall County was 13.79 percent. However, the table indicated that a 4-percent decrease would raise the percentage of total valued property to 14.07 percent.
The board's concern was focused on counties that contained roughly equal percentages of residential and agricultural property, or a higher percentage of residential property. Referring to the shift that could result from a reduction of the assessed residential values, one board member noted that
where it's close to 50/50 or more residential, substantially different ranges of residential versus ag land, that it's pretty clear that if you make an adjustment to residential you get a shift, and if you get a shift, then it puts ... you out of sync with your neighboring counties on ag land to ag land, and that can cause some uncertain results for some taxing districts and you can't develop a matrix to show exactly how that would work so that you can fix it so you wouldn't end up with potentially some major shifts.
On August 15, the board reconvened and further discussed the tax shift ramifications of certain counties. The board again referred to the table created by the Nebraska Department of Revenue.
Hall County Supervisor Quandt was present at this proceeding and spoke to the board concerning the tax shift. Quandt indicated that according to his figures, the breakdown of total land value in Hall County consisted of 56.5 percent residential, 23.4 percent commercial, and 20.1 percent agricultural. He then told the board that a reduction of 6 percent in the assessed value of residential property would create a tax shift increasing the percentage of agricultural land by .7 percent to 20.8 percent of total land value for the county.
The board ultimately concluded that a reduction in residential property values was likely to create a tax shift in Hall County and would result in imposing a greater tax burden on agricultural property owners both in Hall County and in the same taxing districts as Hall County. The board noted that the tax shift would be much higher within the school districts as compared to the shift that results within the county.
The board also reached this same conclusion for Dawson, Hamilton, and York Counties. This conclusion was based on the fact that these counties contained both a significant amount of residential land and agricultural land. Therefore, the board adopted a motion to readjust the assessed residential values of these counties back to their original levels.
The board did not readjust the assessed value of residential property in Frontier County because it contained such a small amount of residential property and, therefore, the tax shift would be minimal. Frontier County is not located within Hall County's community college taxing district.
The board's final order reduced the valuation of four counties. Sarpy County, with an indicated valuation of 94 percent, was decreased 5 percent. Frontier County, with an indicated valuation of 100 percent, was decreased 8 percent. Rock County, with an indicated valuation of 99 percent, was decreased 8 percent. Keya Paha County, with an indicated valuation of 100 percent, was decreased 9 percent.
Neb. Const. art. VIII, § 1, provides that necessary revenue shall be raised by taxation in such a manner as the Legislature may direct. However, this constitutional provision also requires that taxes be levied by valuation uniformly and proportionately upon all real property as defined by the Legislature.
Also pursuant to Neb. Const. art. VIII, § 1(4), the Legislature may declare agricultural land as a distinct class for purposes of taxation, and may provide for a different taxing method for agricultural land that is not uniform with other classes of property, but which results in values that are uniform within the class of agricultural land. The Legislature has in fact declared agricultural land as a separate and distinct class for purposes of property taxation. Neb.Rev. Stat. § 77-201(2) (Cum.Supp.1994).
*170 The Legislature has charged the board with the responsibility and duty to give effect to the constitutional requirement that all taxes be levied uniformly and proportionately upon all real property.
Pursuant to Neb.Rev.Stat. §§ 77-505 et seq. (Cum.Supp.1994), the board is given the power to equalize the values of all real property located in the state. Section 77-506 provides:
Pursuant to section 77-505, the State Board of Equalization and Assessment shall have the power to increase or decrease the value of a class or subclass of real property of any county or tax district or real property valued by the state. Such increase or decrease shall be made by a percent.
The object of the law of uniformity in taxation is accomplished if all of the property within the taxing jurisdiction is assessed at a uniform standard of value. Carpenter v. State Board of Equalization & Assessment, 178 Neb. 611, 134 N.W.2d 272 (1965).
In an appeal from the board, an appellate court searches only for errors appearing on the record, i.e., whether the decision conforms with the law; is supported by relevant and competent evidence; and was not arbitrary, capricious, or unreasonable. County of Adams v. State Bd. of Equal., 247 Neb. 179, 525 N.W.2d 629 (1995).
Moreover, the board has a wide latitude of judgment and discretion in equalizing the assessment of property. Box Butte County v. State Board of Equalization & Assessment, 206 Neb. 696, 295 N.W.2d 670 (1980).
"`[T]he presumption is that the Board faithfully performed its duties and the burden is upon the appellant to prove that the action of the Board was erroneous, arbitrary, capricious, and contrary to the law.'" Id. at 709, 295 N.W.2d at 679.
This court has further held, "`In order to reverse the order of the Board, we would be required to hold the Board utterly failed to follow a reasonable course of action....'" Id.
However, this court has also noted that the board's power is not unlimited. "If the state board fails to follow the statute and acts without authority, proper evidence, or due investigation or for any other reason renders a decision which is not based upon the facts, or is not according to law, its order will be reversed." County of Blaine v. State Board of Equalization & Assessment, 180 Neb. 471, 475, 143 N.W.2d 880, 883 (1966). The record of the proceedings before the board must be sufficient to sustain the action taken by the board. County of Gage v. State Board of Equalization & Assessment, 185 Neb. 749, 178 N.W.2d 759 (1970).
Hall County essentially has set forth two arguments on appeal. First, Hall County contends that the board acted arbitrarily and capriciously by failing to reduce Hall County's assessed value of residential property to the level of the counties that had the lowest values within the same community college tax district.
Second, Hall County contends that the board acted arbitrarily and capriciously by reducing the valuation levels of Sarpy, Rock, Frontier, and Keya Paha Counties without also reducing the valuation of Hall County. Hall County, in its petition for reduction, also alleged that the act of the board in modifying the range of valuation was arbitrary and capricious. However, Hall County has not asserted this argument on appeal.
In response, the board contends that it did not act arbitrarily and capriciously in refusing to reduce the residential property valuations. The board argues that it had a legitimate concern supported by the record that an assessed residential value reduction would result in unintended tax shifts from residential to agricultural property within Hall County and within the overlapping taxing districts. The board further argues that a reduction in the assessed value of agricultural land to remedy a potential tax shift would also result in altering tax burdens for agricultural land across county lines.
Regarding the community college district in which Hall County is located, the record indicates that five counties within the district had an assessed residential property value of *171 89 percent. However, the record also indicates that six counties had equal or greater assessed residential values than that of Hall County's 98 percent. Moreover, the average percentage of the aggregate level of assessed residential property values for the counties located in this tax district is 94.76 percent.
This court has never required that the assessed values between counties be adjusted so as to be exactly equal or to be calculated with mathematical precision. "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." County of Gage, 185 Neb. at 756, 178 N.W.2d at 764.
This court, in Carpenter v. State Board of Equalization & Assessment, 178 Neb. 611, 619, 134 N.W.2d 272, 278 (1965), stated:
[I]t can probably always be demonstrated that the Board, in dealing with the intangible concepts of valuation and uniformity, could never reach any mathematically precise result. Such a yardstick or criterion of equalization can never be accomplished. Approximation, both as to value and uniformity, is all that can be accomplished. [Citation omitted.] And, we have held that the object of the law of uniformity is accomplished if all of the property within the taxing jurisdiction is assessed at a uniform standard of value.

(Emphasis in original.)
All of the counties within the community college taxing district fall within the parameters set by the board. The assessed values of residential property cover the whole range of 89 percent to 100 percent. Hall County's value is not of such a discrepancy from other counties in this taxing district so as to conclude that the board did not accomplish uniformity.
Moreover, when determining whether to reduce Hall County's assessed values to conform with the lower counties in the district, the board analyzed the potential major tax shift ramifications that could arise within taxing districts. Hall County, however, failed to produce any evidence to show that the board's findings as to the potential tax shifts were erroneous or arbitrary. The board concluded that the tax shifts could be significant in the taxing district, and Hall County has not shown this court any evidence to the contrary. In sum, the board acted reasonably in refusing to reduce Hall County residential property values based on community college taxing district grounds. Nor did the Board act arbitrarily by reducing other counties' assessed residential property values while refusing to reduce Hall County's values. The record clearly supports the rationale behind reducing these other counties' assessed residential values.
Regarding Sarpy County, the board concluded that a reduction was required to prevent a significant inequality between Sarpy County and Douglas County. This decision was supported by extensive evidence presented by Sarpy County.
Regarding the rural counties, the board determined that tax shift concerns for these counties were minimal based on the small amount of residential property located in these counties. The board concluded that reduction was feasible without creating inequalization. Again, Hall County has failed to demonstrate how these reductions result in capricious, arbitrary behavior by the board.
In conclusion, the board concluded that by reducing Hall County's assessed valuation of residential property, potential inequalization, rather than greater equalization, could result. This finding is supported by the record of the hearings. Hall County has failed to present sufficient evidence to refute the board's findings regarding the potential tax shifts.
Therefore, the board's decision to maintain Hall County's residential property at an assessed value of 98 percent was not arbitrary or capricious. We affirm.
AFFIRMED.
