OPINION OF THE COURT
ROBERTS, Justice.
This is a dispute between a taxpayer and the Board of Revision of Taxes of Philadelphia over the assessment of real property. At issue is whether the Court of Common Pleas of Philadelphia applied a proper method of calculating the taxing district’s “common level” ratio of assessments to fair market values. Unlike the Commonwealth Court, we are of the view that the court of common pleas committed neither error of law nor abuse of discretion. Hence we reverse.
I
The concept of common-level ratio was fully set forth in Deitch Co. v. Allegheny County Board of Property Assessment, 417 Pa. 213, 209 A.2d 397 (1965). There, based on the uniformity-of-taxation requirement of our Constitution, art. VIII, § 1, and “the principle that a taxpayer should pay no [142]*142more or no less than his proportionate share of the cost of government,” 417 Pa. at 220, 209 A.2d at 401, this Court held that an owner of property is entitled to have his assessment reduced to conform with the common-level of assessments in the taxing district. Id. See Siegal v. City of Newark, 38 N.J. 57, 183 A.2d 21 (1962); Comment, “The Road to Uniformity in Real Estate Taxation: Valuation and Appeal,” 124 U.Pa.L.Rev. 1418 (1976); Note, “Inequality in Property Tax Assessments: New Cures for an Old 111,” 75 Harv.L. Rev. 1374 (1962). In explaining the term “common level,” Deitch stated:
“Where the evidence shows that the assessors have applied a fixed ratio of assessed to market value throughout the taxing district, then that ratio would constitute the common level. However, where the evidence indicates that no such ratio has been applied, and that ratios vary widely in the district, the average of such ratios may be considered the ‘common level’. Siegal v. City of Newark, supra, at 64, 183 A.2d at 24. Furthermore, it may be that the evidence will show some percentage about which the bulk of individual assessments tend to cluster, in which event such percentage might be acceptable as the common level. Ibid.”
417 Pa. at 220-21, 209 A.2d at 401 (footnote omitted) (emphasis in original).
This “common level” requirement does not permit a taxing district to apply one assessment-to-fair-market-value ratio to one use-type of property such as residential and a different ratio to another use-type such as commercial or industrial. Rather, “all properties are comparable in constructing the appropriate ratio of assessed value to market value. This is because the uniformity requirement of the Constitution of Pennsylvania has been construed to require that all real estate is a class which is entitled to uniform treatment.” 417 Pa. at 223, 209 A.2d at 402 (citing cases). Accord, F. W. Woolworth Co. Tax Assessment Case, 426 Pa. 583, 235 A.2d 793 (1967); McKnight Shopping Center, Inc. v. Allegheny County Board of Property Assessment, 417 Pa. 234, 209 A.2d 389 (1965).
[143]*143Practical considerations of course prohibit the construction of a common-level ratio by way of an evaluation of the assessment and fair market value of each and every parcel of realty in the taxing district. Thus Deitch permits the construction of the common-level ratio by “any relevant evidence.” 417 Pa. at 223, 209 A.2d at 403. Specifically recognized as a means of constructing the common-level ratio are sales data.
“It would be . . . satisfactory to produce evidence regarding the ratios of assessed values to market values as the latter are reflected in actual sales of any other real estate in the taxing district for a reasonable period prior to the assessment date. Thus, for example, the taxpayer’s expert witness or witnesses could select a number of recent representative sales and offer testimony with respect to such sales as proof of the ratio in the taxing district.”
Id.
Both parties have chosen to utilize sales data to construct their proposed ratios. However, the parties have chosen different methods to analyze the data. The present disagreement is over which method assures the “representative” quality of the sales data.
II
Taxpayer, appellee Keebler Company, owns approximately eleven acres of industrial realty and buildings of nearly 350,000 square feet. For the 1976 tax year, taxpayer’s property was assessed at $1,655,400. On taxpayer’s appeal, appellant Board of Revision of Taxes upheld the assessment.
Taxpayer appealed the Board’s determination to the court of common pleas. Taxpayer alleged that the fair market value of the property is no more than $2,105,000, and that Philadelphia assessors utilize a ratio no greater than 40% of market value. Multiplication of the alleged maximum fair market value and the alleged maximum ratio produces $842,000, an amount which taxpayer contends is the maximum permissible assessment under Deitch. Thus taxpayer alleged that the proper assessment of its property “should be [144]*144substantially less than $1,655,400,” the amount actually assessed. Taxpayer similarly appealed the assessment of its property for the tax years 1977 and 1978.
The court of common pleas consolidated these appeals and the appeals of many other taxpayers who had challenged the assessments of their properties for the tax years 1975 through 1978. Hearings were held to determine the common-level ratios of assessments to fair market values for those tax years. Thus far only the common-level ratios have been addressed by the court of common pleas. (Fair market values of the properties of the many taxpayers, including Keebler, have not yet been determined.) At the hearings, the parties agreed that although the Board has attempted to utilize an assessment-to-fair-market-value ratio of 50%, in actuality a ratio of less than 50% was utilized for the tax years in question. Both sides presented expert testimony to establish their respective positions on the ratios.
Taxpayer presented Dr. Robert Edelstein as an expert witness. Dr. Edelstein believed it necessary to exclude from the raw sales data those sales which were not arm’s length transactions so that the remaining, working data would provide an accurate sample of fair market values in the community. Thus, for .example, Dr. Edelstein eliminated from the raw sales data transfers between relatives, tax-free transfers such as those involving a governmental unit, and transfers involving unfinished residences. Also excluded were those transactions whose ratios were more than three “standard deviations” from the “mean.” This statistical procedure was designed to assure that inferences from the data would not be unfairly affected by extreme cases. Remaining were “arm’s length transactions,” defined by Dr. Edelstein as those sales with ratios ranging from 20% to 100%, as well as those with ratios of 20% or less.
From the remaining data, Dr. Edelstein calculated the common-level ratio simply by dividing the sum of the assessments of the properties sold by the sum of the respective [145]*145selling prices.1
Free access — add to your briefcase to read the full text and ask questions with AI
OPINION OF THE COURT
ROBERTS, Justice.
This is a dispute between a taxpayer and the Board of Revision of Taxes of Philadelphia over the assessment of real property. At issue is whether the Court of Common Pleas of Philadelphia applied a proper method of calculating the taxing district’s “common level” ratio of assessments to fair market values. Unlike the Commonwealth Court, we are of the view that the court of common pleas committed neither error of law nor abuse of discretion. Hence we reverse.
I
The concept of common-level ratio was fully set forth in Deitch Co. v. Allegheny County Board of Property Assessment, 417 Pa. 213, 209 A.2d 397 (1965). There, based on the uniformity-of-taxation requirement of our Constitution, art. VIII, § 1, and “the principle that a taxpayer should pay no [142]*142more or no less than his proportionate share of the cost of government,” 417 Pa. at 220, 209 A.2d at 401, this Court held that an owner of property is entitled to have his assessment reduced to conform with the common-level of assessments in the taxing district. Id. See Siegal v. City of Newark, 38 N.J. 57, 183 A.2d 21 (1962); Comment, “The Road to Uniformity in Real Estate Taxation: Valuation and Appeal,” 124 U.Pa.L.Rev. 1418 (1976); Note, “Inequality in Property Tax Assessments: New Cures for an Old 111,” 75 Harv.L. Rev. 1374 (1962). In explaining the term “common level,” Deitch stated:
“Where the evidence shows that the assessors have applied a fixed ratio of assessed to market value throughout the taxing district, then that ratio would constitute the common level. However, where the evidence indicates that no such ratio has been applied, and that ratios vary widely in the district, the average of such ratios may be considered the ‘common level’. Siegal v. City of Newark, supra, at 64, 183 A.2d at 24. Furthermore, it may be that the evidence will show some percentage about which the bulk of individual assessments tend to cluster, in which event such percentage might be acceptable as the common level. Ibid.”
417 Pa. at 220-21, 209 A.2d at 401 (footnote omitted) (emphasis in original).
This “common level” requirement does not permit a taxing district to apply one assessment-to-fair-market-value ratio to one use-type of property such as residential and a different ratio to another use-type such as commercial or industrial. Rather, “all properties are comparable in constructing the appropriate ratio of assessed value to market value. This is because the uniformity requirement of the Constitution of Pennsylvania has been construed to require that all real estate is a class which is entitled to uniform treatment.” 417 Pa. at 223, 209 A.2d at 402 (citing cases). Accord, F. W. Woolworth Co. Tax Assessment Case, 426 Pa. 583, 235 A.2d 793 (1967); McKnight Shopping Center, Inc. v. Allegheny County Board of Property Assessment, 417 Pa. 234, 209 A.2d 389 (1965).
[143]*143Practical considerations of course prohibit the construction of a common-level ratio by way of an evaluation of the assessment and fair market value of each and every parcel of realty in the taxing district. Thus Deitch permits the construction of the common-level ratio by “any relevant evidence.” 417 Pa. at 223, 209 A.2d at 403. Specifically recognized as a means of constructing the common-level ratio are sales data.
“It would be . . . satisfactory to produce evidence regarding the ratios of assessed values to market values as the latter are reflected in actual sales of any other real estate in the taxing district for a reasonable period prior to the assessment date. Thus, for example, the taxpayer’s expert witness or witnesses could select a number of recent representative sales and offer testimony with respect to such sales as proof of the ratio in the taxing district.”
Id.
Both parties have chosen to utilize sales data to construct their proposed ratios. However, the parties have chosen different methods to analyze the data. The present disagreement is over which method assures the “representative” quality of the sales data.
II
Taxpayer, appellee Keebler Company, owns approximately eleven acres of industrial realty and buildings of nearly 350,000 square feet. For the 1976 tax year, taxpayer’s property was assessed at $1,655,400. On taxpayer’s appeal, appellant Board of Revision of Taxes upheld the assessment.
Taxpayer appealed the Board’s determination to the court of common pleas. Taxpayer alleged that the fair market value of the property is no more than $2,105,000, and that Philadelphia assessors utilize a ratio no greater than 40% of market value. Multiplication of the alleged maximum fair market value and the alleged maximum ratio produces $842,000, an amount which taxpayer contends is the maximum permissible assessment under Deitch. Thus taxpayer alleged that the proper assessment of its property “should be [144]*144substantially less than $1,655,400,” the amount actually assessed. Taxpayer similarly appealed the assessment of its property for the tax years 1977 and 1978.
The court of common pleas consolidated these appeals and the appeals of many other taxpayers who had challenged the assessments of their properties for the tax years 1975 through 1978. Hearings were held to determine the common-level ratios of assessments to fair market values for those tax years. Thus far only the common-level ratios have been addressed by the court of common pleas. (Fair market values of the properties of the many taxpayers, including Keebler, have not yet been determined.) At the hearings, the parties agreed that although the Board has attempted to utilize an assessment-to-fair-market-value ratio of 50%, in actuality a ratio of less than 50% was utilized for the tax years in question. Both sides presented expert testimony to establish their respective positions on the ratios.
Taxpayer presented Dr. Robert Edelstein as an expert witness. Dr. Edelstein believed it necessary to exclude from the raw sales data those sales which were not arm’s length transactions so that the remaining, working data would provide an accurate sample of fair market values in the community. Thus, for .example, Dr. Edelstein eliminated from the raw sales data transfers between relatives, tax-free transfers such as those involving a governmental unit, and transfers involving unfinished residences. Also excluded were those transactions whose ratios were more than three “standard deviations” from the “mean.” This statistical procedure was designed to assure that inferences from the data would not be unfairly affected by extreme cases. Remaining were “arm’s length transactions,” defined by Dr. Edelstein as those sales with ratios ranging from 20% to 100%, as well as those with ratios of 20% or less.
From the remaining data, Dr. Edelstein calculated the common-level ratio simply by dividing the sum of the assessments of the properties sold by the sum of the respective [145]*145selling prices.1 This calculation is called a “weighted ratio.” The ratio is “weighted” in the sense that the contribution of the ratio of each parcel of land to the overall ratio depends upon the parcel’s assessment and selling price. The overall ratio would be “unweighted” if the ratios of the parcels were averaged.2
Like Dr. Edelstein, the Board’s expert witness, Dr. Raymond Richman, worked with those properties with ratios ranging from 20% to 100%. However, unlike Dr. Edelstein, Dr. Richman did not include transactions with ratios of 20% or less. Dr. Richman believed that this group of sales data included “mismatches” — properties in poor condition on the assessment date and assessed accordingly, but subsequently rehabilitated and sold during the same taxing year for a price much higher than the original, pre-rehabilitation fair market value.
Far more substantial a difference in the two experts’ methods was Dr. Richman’s effort to adjust the remaining sales data by use-type. Dr. Richman presented figures at the hearing indicating that the proportion of residential properties in the sales sample significantly exceeded the proportion of residential properties in the community, while commercial and industrial properties appeared in the sample in lower proportions than they appear in the community. For example, in 1975, residential properties occupied 67.27% of total sales prices, while they occupied 54.04% of city-wide fair market values. For that same year, commercial and [146]*146industrial properties occupied only 7.66% and 4.29% of total sales prices, respectively. However, they occupied 17.13% and 9.68% of city-wide fair market values, variances in a direction opposite from the residential variance.3
In Dr. Richman’s view, these disproportionate relationships distort the inferences to be drawn from the sales data because residential properties tend to have lower ratios than commercial and industrial properties. For example, again in 1975, residential properties were assessed at a ratio of 36.1%, while commercial and industrial properties were assessed at ratios of 49.4% and 44.0%, respectively.4 Dr. Richman expressed the view that a weighted-average method such as the one employed by taxpayer’s expert, which did not adjust for these disproportionate relationships, produces misleadingly low common-level ratios.
To adjust, Dr. Richman “stratified” his sales data by use-type — residential, hotels and apartment buildings, stores with dwellings, commercial, industrial, and vacant. Dr. Richman then calculated the ratio for each use-type by determining the ratio of each transaction within the use-type, adding these ratios, and then averaging them.5 The quotient, an “unweighted” ratio, was then employed to determine the fair market values within each use-type by dividing total assessments in the use-type by the use-type’s unweighted ratio.6 All assessments, regardless of use-type, were then added, as were all fair market values as previously calculated. The division of all assessments by all fair [147]*147market values yields the common-level ratio as calculated by Dr. Richman.
Dr. Richman indicated that his calculation of the common-level ratio by way of an unweighted ratio for each use-type was not necessarily a statistically ideal technique. However, he expressed the view that in the circumstances it constituted the best of several statistical techniques available. According to Dr. Richman, “within each class in the actual sample of sales, the distribution is . . . not representative of the class of property in Philadelphia. As a result of that, I fall back on the ratio which I believe is the most neutral, and that is the unweighted mean ratio, in calculating market value.”7 Richman added that the margin of his error, from a statistical standpoint, was approximately 2.5%.
Thus, in sum, both Dr. Edelstein for taxpayer and Dr. Richman for the Board utilized sales data. However, Dr. Edelstein included sales with ratios 20% or less while Dr. Richman excluded them. Further, unlike Dr. Edelstein, Dr. Richman “stratified” the data by use-type and, in an intermediate step, calculated each use-type’s unweighted ratio to determine the overall common-level ratio. These differences in methods resulted in the following common-level ratios for the tax years in question:
1975 1976 1977 1978
Dr. Edelstein (for taxpayer) 36.8% 37.8% 33.9% 34.4%
Dr. Richman (for Board) 48.94% 48.48% 46.16% 45.67%.8
Ill
The court of common pleas found the proper ratios to be:
1975 1976 1977 1978
Court of Common Pleas 47.44% 46.98% 44.66% 44.17%.
The court’s findings represent only a slight departure from the ratios offered by Dr. Richman for the Board. The court accepted Dr. Richman’s method in all relevant respects, including the stratification of property by use-type and the [148]*148calculation of each use-type’s unweighted ratio. Based on all the evidence presented, the court agreed with Dr. Rich-man that stratification was necessary to adjust for the disproportionately large level of residential sales in the sample and that calculation of each use-type’s unweighted ratio was appropriate. In accepting the Board’s method over taxpayer’s, the court observed:
“The utilization of this method prevents much of the distortion resulting from the overrepresented residential properties and the underrepresented commercial and industrial properties in the sample. The taxpayers’ use of this sample to calculate the weighted ratio is not the preferred method; that calculation is too sensitive to the non-representative dollar values in the sample.
On the other hand, the Board’s use of the weighted ratio not for just the sample, but for the entire City, is significantly less sensitive to those dollar values.”
The court modified Dr. Richman’s exclusion of all sales with ratios of 20% or below. According to the court, Dr. Richman expressed valid concern that these transactions are suspect, but unreasonably concluded that all such transactions should be excluded. The court determined that one half of the 20%-or-lower ratio transactions should have been included in Dr. Richman’s data base. Thus, taking into account Dr. Richman's stated margin for error, the court reduced Dr. Richman’s determinations by a fractional amount to reflect a partial inclusion of the 20%-or-less ratio transactions.9
On taxpayer’s appeal, a majority of the Commonwealth Court rejected the Board’s method. According to the Commonwealth Court, the “stratification” technique employed by the Board is based on a division of realty into classes, which is proscribed by Deitch, while taxpayer’s method is “the one commonly utilized in Pennsylvania and specifically approved by the Pennsylvania Supreme Court.” [Kenney v. Keebler Co.] 53 Pa.Cmwlth. 507, 511, 419 A.2d 210, 212 (1980) (citing Deitch). This Court granted the Board’s petition for allowance of appeal.
[149]*149IV
As this record amply demonstrates, raw sales data are not always reliable substitutes for the fair market value of a taxing district. As a leading reference manual prepared by assessors points out,
“[s]ales price data are valid and useful only to the extent that they represent fair market values. Unfortunately, of course, sales prices and market values are two different things. It is convenient to think of the market value of a property as an unknown quantity, and the sale price of a property as evidence of market value. In some cases, sales prices provide very good evidence of market values, and in other cases they provide only poor evidence. The latter cases need either to be flagged with error or warning messages or, if possible, to be adjusted in such a manner that they provide useful approximations of market values.”
International Association of Assessing Officers, Improving Real Property Assessment at 106 (1978) (emphasis in original).
Fully recognizing the hazards of sales data, the trial court, in harmony with the “representative” sales data requirement of Deitch, properly reviewed the sales data with which both experts worked. With the trial court’s approval, both experts here excluded transfers for nominal consideration, among relatives and the like. Thus it was assured that the inferences drawn from the data were not unreasonably affected by transactions which were not at arm’s length. This preliminary step in both experts’ methods, approved by the trial court, resembles the method employed by the State Tax Equalization Board, see 61 Pa.Code § 603.31(b), which is statutorily obliged to utilize market data to determine market values of school districts for state subsidy purposes. See Act of June 27, 1947, P.L. 1046, § 1 et seq., 72 P.S. § 4656.1 et seq. (1968).
Moreover, the court of common pleas, again in harmony with Deitch, carefully reviewed the sales data on which the experts disagreed. Pursuant to this review, the court deter[150]*150mined that a fractional share of transfers with ratios of 20% or less should have been included by the Board’s expert and that the remaining share should have been excluded by taxpayer’s expert.10
By concluding that taxpayer’s method is “the one commonly utilized in Pennsylvania,” and that the court of common pleas erred in accepting remaining aspects of the Board expert’s method, the Commonwealth Court would require the trial court to terminate any further inquiry into the “representative” quality of sales data. However, the Commonwealth Court’s conclusion overlooks the danger that sales data may not provide a reasonably random sample of all properties in the taxing district. Particular sales data are permissibly employed because sales prices can provide a reasonable forecast of fair market values of properties in the taxing district. Without adjustments beyond the elimination of non-arm’s-length transactions, there is a serious risk that the calculations of common-level ratios will reflect not the taxing district, but only the sample of properties sold.
This difficulty is best illustrated by what has become the classic, textbook case of unrandom sampling. In 1936, the now-defunct Literary Digest sought to predict the results of that year’s presidential election. Sample voters were selected from among owners of telephones and owners of automobiles. Based on its poll taken from the sample voters, the Digest predicted that Alfred Landon would defeat Franklin Roosevelt by a landslide. The opposite was true.
The Digest was the victim not of voters’ last-minute change of heart, but of its own unsound sampling technique. If only those who owned telephones and automobiles had been permitted to vote, the Digest might well have forecast the 1936 election correctly. However, many more than owners of telephones and automobiles comprised the electorate than were included in the Digest’s sample. Those excluded from the poll provided Roosevelt his greatest support. See Freund & Williams’ Modern Business Statistics at 271 (Perles & Sullivan rev. 1969).
[151]*151The evidence of the Board’s expert established that, like the ill-fated Literary Digest poll, taxpayer’s sales data were not properly adjusted to reflect the entire taxing district. We are satisfied that the trial court properly rejected taxpayer’s method and thus avoided the attendant distorted inferences.
Unlike the Commonwealth Court, we perceive no inconsistency between the Board expert’s stratification of sales data by use-type and Deitch’s prohibition against different ratios for different use-types. To the contrary, the Board expert’s stratification technique was specifically designed to avoid the computation of a common-level ratio which would unduly reflect the ratios of residential properties. If anything is “commonly utilized in Pennsylvania” it is stratification. See 61 Pa.Code § 603.21(1) (State Tax Equalization Board “analyz[es] and tabulates] taxable real property assessments by use of property”).
We also are unpersuaded by taxpayer’s argument against the Board expert’s use of an “unweighted ratio.” Although a weighted ratio has been termed the “single most appropriate measure for estimating the full cash value of all real property in a particular use class or stratum of properties,” Improving Real Property Assessments, supra, at 127, it has also been said that “[t]he appropriateness of the weighting feature ... is a matter of opinion with respect to the measurement of assessment performance.” Id. As has already been seen, the Board expert’s use of an unweighted ratio was but an intermediate step in the calculation of the overall common-level ratios. The Board’s expert expressed the opinion that this intermediate step was a statistically sound means of achieving the critical end of adjusting for imperfections in the sales data. Thus taxpayer’s contention is merely a challenge to the trial court’s decision to accept as credible the Board expert’s view. Like other challenges to a fact-finder’s resolution of credibility supported by the evidence, this contention cannot prevail. See, e. g., Tinicum Real Estate Holding Corp. v. Commonwealth, Dep’t of Transp., 480 Pa. 220, 232, 389 A.2d 1034, 1040-41 (1978).
[152]*152Order of the Commonwealth Court reversing the ratio determinations of the court of common pleas is reversed.
LARSEN, J., files a dissenting opinion.
O’BRIEN, C. J., and WILKINSON, J., did not participate in the consideration or decision of this case.