Cutter, J.

The appellant (Stores) sought from the Somerville assessors for certain of the years 1964, 1965, *555 and 1966 abatements of real estate taxes on three parcels of land. When the assessors failed to act on the abatement applications, Stores (see 6. L. c. 59, §§ 64, 65) filed with the Appellate Tax Board (the board) petitions under the formal procedure. Each petition alleged not only that the particular property was overvalued by the assessors in excess of the full and fair cash value, but also that Stores was aggrieved by deliberate, disproportionate, and discriminatory assessments.

On May 15, 1968, the board directed Stores “to make within five days a further and better statement of the nature of . . . ^Stores’] claims of a disproportionate assessment” conforming to “the standards of pleading set forth in” Stone v. Springfield, 341 Mass. 246, 251, and Shoppers’ World, Inc. v. Assessors of Framingham, 348 Mass. 366, 370. Stores filed such a statement specifying, among other matters, that for each of the years 1964, 1965, and 1966, the aggregate assessed value of all the properties sold in Somerville in the next prior calendar year was a percentage between 38.3% (1966) and 45.7% (1964) of the aggregate fair cash value of those properties sold, whereas during these years, Stores contends, its three groups of properties were assessed at 124.2%, 97.2%, and 74% of their respective fair cash values.

Evidence of most of the real estate sales in Somerville during the years 1960 to 1966, inclusive, was presented at frequently postponed hearings before the board. 1 A certified copy of each individual recorded deed of Somerville real estate in those years was introduced. There was also introduced a tabulation of these sales giving (for each sale, deed, and parcel of land) the following information: (a) the month and year of sale, (b) the street location, (c) the record book and page, (d) the value of affixed revenue stamps, (e) the sales price thereby indicated, (f) the assessment as of the January 1 next following, (g) later change (if any) in the assessment, and (h) the ratio of assessed value to sales price. In Stores’ brief this evidence is summarized for the years *556 1964 to 1966 inclusive, 2 apparently on the basis of the sales listed in the compilation.

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In its brief Stores further breaks down the statistics shown in the tabulation to indicate the number of parcels within various ranges of ratios of assessment to sales price in each of the years 1964, 1965, and 1966, as follows: 3

TABLEB

Assessment-Sales Parcels of Property Having Column (1)

Price Ratio Assessment-Sales Price Ratio

(D (¿9 (8) (4) 1964 * 1965 1966 o%-19% 4 3 7 20% 29% 32 46 53 30% 39% 135 125 116 40% 49% 32 60 42 50%-59% 20 12 21 60% - or over 35 23 26

*557 Assessors of Somerville also testified. Chairman. George J. Moran, Jr., gave testimony that Somerville assessments made by him were based on visual inspection of each parcel, whether residential or commercial; that he (in the assessment process) does not take sales prices into consideration; and that he would not do so even if he knew what they were.* 4 He uses the same visual method for all types of property. He did not know whether Somerville residential, commercial, and industrial property was assessed at full and fair cash value in the years 1964 to 1966. He does not use (a) capitalization of income or (b) reproduction cost less depreciation as a valuation method. He sometimes uses the value of comparable properties as an aid. There was testimony from another assessor that with reference to assessments in Somerville, for twenty years “the policy has been the same, fair market value,” and the assessments have remained “[practically” the same. The assessors were aware of the information in their records concerning sales prices.

There was substantial evidence before the board concerning the fair cash value of each of Stores’ three groups of properties. The board found that the Group “A” properties (5 Middlesex Avenue and Mystic Avenue) were over-assessed by $352,200. It also concluded that the Group “B” (Middlesex Avenue) and Group “C” (57R Mystic Avenue) properties were not assessed at more than their *558 fair cash value. The various views on value are set out in the margin. 5

On May 22, 1968, Stores requested the board to find as a fact and also to “rule as . . . matter of law that the evidence supports an inference of fractional, unequal, and discriminatory assessments in . . . Somerville during the years in issue and that the . . . [assessors have] the burden of going forward to show that there . . . [were] no such fractional, unequal, and discriminatory assessments.” Each request for ruling was denied when the board announced its decisions. “On the issue of disproportionate assessment,” the board entered in each case a decision for the assessors because Stores “has not sustained its burden of proof and further . . . wrongfully used a market data approach to valuation to determine the fraction of alleged disproportionate assessments and at the same time used a capitalization method of valuation of its own property to form the basis of an abatement.”

Stores thereupon claimed an appeal to this court, assigning as error that the board (1) incorrectly failed to rule that the evidence supported an inference of fractional, unequal and discriminatory assessments; (2) ruled wrongly that Stores had not sustained its burden of proof of disproportionate assessment; and (3) erred in ruling that Stores im *559 properly used inconsistent valuation methods. No appeal has been taken from the board’s decisions on the issue of fair cash value.

1. The proper method of assessment of real property is at 100% of fair cash value. 6 See Part II, c. 1, § 1, art. 4, of the Constitution of the Commonwealth, and also art. 10 of the Declaration of Rights; G. L. c. 59, §§ 38, 52; Bettigole v. Assessors of Springfield, 343 Mass. 223, 231-232; Shoppers’ World, Inc. v. Assessors of Framingham, 348 Mass. 366,

371-372, and cases cited; Bennett v. Assessors of Whitman, 354 Mass. 239, 240. The requirement that real estate assessments be proportional is firmly established. In the Shoppers’ World case (at p. 377), we held that a taxpayer may show, if he can, that “substantially all other . . . properties” in a city are assessed as a matter of policy at a lower percentage of fair cash value than his own, and may prove “the assessors’ general policy and standards of assessment of other properties ... in relation to full, fair cash value.” We went on to say (pp. 377-378), “If the taxpayer establishes improper assessment of such number of . . . properties (at less than fair cash value and on a basis discriminating against the taxpayer) as to support an inference that there was a scheme of such assessment, then the assessors will have the burden of going forward to show that there has been no scheme of discriminatory assessment. If, on all the evidence, such a scheme is established, the taxpayer may be granted an abatement . . . which will make the taxpayer’s assessment proportional to other assessments, on a basis which reaches results as close as is practicable to those which would have followed application by the assessors of the proper statutory assessment principles. No practical difficulties should result ... if assessors assess each item of taxable property at its full, fair cash value to the best of their ability and pursuant to their honest judgment” (emphasis supplied). Stores’ requests for rulings filed May 22, 1968, and its *560 assignments of error are obviously based on the language •just quoted.

Stores, within ten days of the board’s decision, did not request the board, as it would have been wise to do, “to make findings and report thereon.” See G. L. c. 58A, § 13 (as amended through St. 1968, c. 120, §§ 2-4; see later amendment by St. 1969, c. 692). The board did not exercise its discretion to write an informative opinion. This would have been desirable in a case likely to be appealed to this court. See Assessors of New Braintree v. Pioneer Valley Academy, Inc. 355 Mass. 610, 612, fn. 1. Nevertheless, the board’s denial of Stores’ requests for rulings sufficiently raises a question of law for our decision.

The evidence was in various respects somewhat disorderly and vague. Stores, however, did show that most real estate sale prices in Somerville during the years immediately preceding the three assessment years (1964-1966) had far exceeded the assessments of the same properties as of the next succeeding January 1. Actual sales are, of course, very strong evidence of fair market value, for they represent what a buyer has been willing to pay to a seller for a particular property. 7 See Massachusetts Gen. Hosp. v. Belmont, 233 Mass. 190, 205-208, 209-210; Brush Hill Dev. Inc. v. Commonwealth, 338 Mass. 359, 364-365. Cf. Commissioner of Corps. & Taxn. v. Worcester County Trust Co. 305 Mass. 460, 462; Newton Girl Scout Council, Inc. v. Massachusetts Turnpike Authy. 335 Mass. 189, 193-197; Commonwealth v. Massachusetts Turnpike Authy. 352 Mass. 143, 147-151. Comparison of the aggregate sales prices with the aggregate tax assessments of those properties in the year following the sale (see Table A, supra), gives strong support to an inference that the substantially consistent aggregate assess *561 ment-aggregate sales price ratio reflects general assessment policy in the city. Particularly is this so (see fn. 2, supra), where indications concerning certain prior years are generally comparable to the figures for the most pertinent years. It is hard to imagine any other method of testing assessment policy likely to be as informative.

Such a method of testing assessments obviously cannot be used to show the ratio of assessments to fair market value in the case of properties which have not been sold. As to properties not sold, other methods of determining fair cash value must be employed. Such methods are not unusual in connection with property tax, inheritance tax, and estate tax valuations or in determining the value of property taken by eminent domain. Since fair cash or market value is the criterion in each instance, valuations based on actual sales reasonably may be compared with valuations determined by experts using their judgment to fix fair cash value, assisted by recognized criteria of value. See McKnight Shopping Center, Inc. v. Board of Property Assessment, 417 Pa. 234, 238-242. See also Re: Appeals of Kents 2124 Atlantic Ave. Inc. 34 N. J. 2d 21, 29-33; Deitch Co. v. Board of Property Assessment, 417 Pa. 213, 221-224; note, 75 Harv. L. Rev. 1374. Cf. Fisher-New Center Co. v. State Tax Commn. 380 Mich. 340, 361-370.

We assume (since no appeal has been claimed) that the parties accept, as representing fair cash value, the board’s valuation of the Group “A” properties. The State board charged with reviewing tax assessments may be expected to try to apply the proper standard of fair cash value. The board’s abated valuation of Stores’ Group “A” properties thus may reasonably be taken as representing an adjusted assessment at 100% of fair cash value. 8 So viewed, this adjusted 100% assessment may be compared (to determine whether there has been discrimination against Stores) with *562 the assessment-sales price ratio developed from considering the assessments and sales prices of the numerous properties sold. The board’s determination (see fn. 5), by granting no abatement, of at least the minimum value of the Group “B” and Group “C” properties, of course, is less readily to be used in such a comparison, even though the board had evidence before it which would have enabled it to determine the fair cash value of those two groups of properties.

The testimony of the assessors (see fn. 4 and related text of this opinion) made no adequate explanation of their failure to permit the trend of actual sales prices to influence their judgment to a greater extent. Some of the assessors purported to give little or no weight to criteria of valuation generally regarded as useful. Their testimony was diffuse and vague, and had little tendency to show that they had made any systematic or coordinated effort to apply (in performing their annual function of valuation) the statutory standard of fair cash value. There is, for example, in the evidence no suggestion that the assessors’ assessment policies have been influenced by considerations such as those discussed in Leto v. Assessors of Wilmington, 348 Mass. 144, 151, fn. 8.

The board improperly denied Stores’ requests for rulings. The evidence, as matter of law, sufficed to support an inference of a scheme of assessment discriminating against this taxpayer. The assessors should have been required to assume “the burden of going forward to show that there . . . [had] been no scheme of discriminatory assessment.” See the Shoppers’ World case, 348 Mass. 366, 377. Sustaining that burden requires an affirmative showing of a reasonable effort to apply the statutory standard of full and fair cash value on a nondiscriminatory and systematic basis, giving appropriate weight to all pertinent criteria. To sustain the burden, the assessment process should be shown to be more than mere exercise of the judgment or whim of individual assessors following visual examination of each particular property. The ultimate burden of persuasion, of course, will remain upon the taxpayer.

*563 2. The decisions are reversed. The cases are to be remanded to the board for further hearing in the light of this opinion, and of what we said in the Shoppers' World case, 348 Mass. 366. In examination of the assessors and their staff, reasonable latitude should be permitted, so that the evidence may disclose what assessment policies are in fact employed, whether statutory standards in fact are applied, and what the assessors’ plans are for achieving an equitable and proportional assessment of properties in Somerville.

So ordered.

Notes

December 4, 13, and 27, 1967, January 29, March 25 and 26, April 16, May 14, 15, 16, 22, 23, and 28 and June 4, 1968.

Some of the 1964 sales seem to have been omitted from this tabulation.

No tabulation appears in Stores’ brief of the data for years 1960 to 1963, but in Stores’ statement filed in answer to the board’s order of May 15,1968, these data were alleged: 1960-1962 — 1,016 sales which in the following January “resulted in assessed valuations of . . . percentages of fair cash value” comparable to the ratio between (a) the assessed values of the properties sold in the year following the sale, and (b) the sales prices realized in Somerville sales in 1963, 1964, and 1965. With respect to 556 sales in 1962, the total sales value was alleged to be $9,091,772. The 1963 assessments of these properties in the aggregate were $4,311,500. This assessment-sales price ratio was 47.4%.

Stores argues that Table B shows not only that, for the pertinent years, property in Somerville (as to which fair cash value was established or indicated by actual sale) “was on the average assessed at less than 50% of fair *557 cash value but that most [such] property in Somerville was for these years assessed at less than 50% of fair cash value while only a relatively small number of [sold] parcels were assessed above 50%, indicating a clear intent to assess the greater majority of [such] taxpayers at a common level of less than 50% and only a few taxpayers at above 50%.”

Chairman Moran also testified that the assessors do not assess at a percentage of full and fair cash value “as such.” There is no set percentage formula. “[I]t is . . . physically impossible to spell out a set percentage because, in my opinion, the percentage would have to be variable to some degree.” Another assessor, who relies on looking at the properties he assesses, does not “ consider selling price,” or capitalization of income, or reproduction cost less depreciation. He does not “know the policies of the whole [b]card” of assessors nor whether all real estate in Somerville is assessed at full and fair cash value, or whether all real estate in the district for which he is responsible is so assessed.

Ratio Ratio

William Robert Abated Abated

Abated Morrissey Foster Assessment Assessment Assessment (Stores* (Assessors* to Morrissey to Foster (1964-1906) expert) expert) Estimate Estimate

Group “A” . 53,376,000 (Note A) $3,000,000 54,660,000 112.5% 72.4%

Group “B” . 51,550,000 2,094,000 4,161,000 74.0% 37.2%

Group “C” 181,800 (Note B) 187,000 262,000 97.2% 69.4%

$5,106,800 55,281,000 $9,083,000 96.7% 56.2%

Note A. The original Group “A” assfessment was $3,727,200.

Note B. It cannot be said, of course, that the board found the fair cash value of the Group *‘B” and “C” properties to be the assessed value of thoseADasdfsasfsdf properties, for on the issue of assessment in excess of fair cash value, the board merely found for the assessors, the appellee. With respect to the properties (Group A) where the board actually found the fair cash value, its conclusion was much closer to the appraisal by Morrissey, Stores’ expert, than to the estimate by Foster, the assessors’ expert.

In the 1970 election the voters rejected a constitutional amendment which would have changed somewhat the rule requiring assessments to be proportional. See 1968 Senate Journal, pp. 1722-1726; 1969 Senate Journal, pp. 1188-1194.

When one considers 852 sales in a city over a three year period there is basis for believing that these, on the average, reflect a market based on arms length negotiations. Although it is unlikely that any large part of all the properties in a city, or particular district of a city, will be sold in any three-year period, the volume of sales here considered represents a substantial sampling, particularly if widely distributed as these sales appear to have been. Most sales listed were at prices strongly suggesting that residential properties had been sold.

We do not now consider whether and to what extent other decisions of the board, fixing (by the granting of abatements) the fair cash value of properties in Somerville in or close to the pertinent years, may be regarded as establishing that some properties in the city are assessed at 100% of fair cash value.