delivered the opinion of the court:
Our State Constitution requires that taxes on real property be levied uniformly by valuation. (Ill. Const. 1970, art. IX, sec. 4(a).) Although more dramatically illustrated in other ways, this is an imperfect world; hence, assessment levels vary. Recognizing this prosaic reality, the legislature has charged the Department of Revenue with equalizing assessments on a county-by-county basis so that (with certain exceptions) the assessed valuation of the real property in each county is, in aggregate, 33⅓% of its fair cash value. (Ill. Rev. Stat. 1985, ch. 120, par. 627.) To carry out this mandate, the *532Department annually calculates an equalization factor, or “multiplier,” for each county.
Richard L. Airey and numerous other Cook County taxpayers appeared at the Department’s hearings on the tentative Cook County multipliers for 1983 and 1984. (See Ill. Rev. Stat. 1985, ch. 120, par. 629a.) A hearing officer overruled their objections to the Department’s methodology, and the Department certified multipliers of 1.9122 and 1.8445, respectively. On administrative review in the circuit court of Cook County (Ill. Rev. Stat. 1985, ch. 120, par. 619; ch. 110, par. 3 — 101 et seq.), certain interveners were permitted to join the existing plaintiffs’ objections. The circuit judge affirmed the Department’s determinations for each tax year, and we allowed the plaintiffs to appeal directly to this court. 103 Ill. 2d R. 302(b).
“[S]carcely a model of statutory draftsmanship” (Hamer v. Kirk (1976), 65 Ill. 2d 211, 218), section 146 of the Revenue Act of 1939 somewhat obtusely outlines the procedure for calculating the multipliers. It requires the Department to compare the assessed valuations of various properties in a county “as revised by boards of review or boards of appeals, as the case may be” to the “fair cash values [of those properties] established through the analysis of property transfers, property appraisals, and such other means as it deems proper and reasonable.” (Ill. Rev. Stat. 1985, ch. 120, par. 627.) The result of these calculations is the median level of assessment in the county; the multiplier is the factor by which the median level of assessment must be multiplied to reach the statutorily required of fair cash value. (Ill. Rev. Stat. 1985, ch. 120, pars. 627, 630.) Thus, 33⅓% divided by the median level of assessment equals the multiplier.
The process is slightly more complicated in Cook County, which pursuant to constitutional authority (Ill. *533Const. 1970, art. IX, sec. 4(b)) classifies property for purposes of taxation (see Cook County Real Property Assessment Classification Ordinance). Each classification has its own required level of assessment varying between 16% and 40% of market value. For Cook County, the Department actually determines the median level of assessment for each of the five major classes of property (as well as one subclass). From these levels, the Department calculates an overall county weighted median level of assessment. In Cook County, as elsewhere, the overall level of assessment must be equalized at 33⅓%.
Section 1(20) of the Revenue Act of 1939 fleshes out the method of determining the median level of assessment known as the “sales ratio study”:
“The term ‘33⅓%’ means 33⅓% of the actual value of real property, as determined by the Department’s assessment to sales ratio studies for the 3 most recent years preceding the assessment year, adjusted to take into account any changes in assessment levels implemented since the data for such studies were collected. In compiling such sales ratio studies the Department shall exclude from the reported sales price of any real property any amounts included for personal property and sales finance charges. ***” Ill. Rev. Stat. 1985, ch. 120, par. 482(20).
Also relevant here is the Real Estate Transfer Tax Act, which provides a data source for the Department’s sales ratio studies. (Ill. Rev. Stat. 1985, ch. 120, par. 1001 et seq.) Section 3 of that Act imposes a tax on the transfer of real property and requires the filing of a declaration form (known as a “green sheet”) for each transfer, which, in addition to various descriptive information on the property and the type of conveyance, includes “sales information questions” and “financing questions”:
“The subject of the sales information questions shall include, but not be limited to, information on compulsory transactions, sales between relatives and related corpora*534tions, contractual sales, and deed or trust document types. In addition, the declaration form shall contain questions regarding the financing of the sale. The subject of the financing questions shall include any direct seller participation in the financing of the sale or information on financing that is unconventional so as to impact the fair cash value received by the seller. The intent of such sales and financing questions shall be to aid in the reduction in the number of buyers required to provide financing information necessary for the adjustment outlined in subsection (24) of Section 1 of this Act. The declaration shall include an appropriate place for the inclusion of special facts or circumstances, if any, and shall include the following data: value of personal property sold with the real estate, sales finance charges (points) paid by the seller, the sales price, type of financing (conventional, YA, FHA, seller-financed, other), down payment, term, interest rate, type and description of interest rate (fixed, adjustable or renegotiable), the year the contract was initiated if a contractual sale, and the name, address and telephone number of the person filling out the real estate transfer declaration.” (Ill. Rev. Stat. 1985, ch. 120, par. 1003.)
After a declaration is completed, the recorder of deeds transmits it to the assessor, “who shall insert on such declaration the most recent assessed value for each parcel of the transferred property, and, at least once during every month, shall transmit all such declarations to the Department.” Ill. Rev. Stat. 1985, ch. 120, par. 1003.
The Department, following section 1(20), used sales ratio studies for the three preceding years — 1980, 1981 and 1982 — to compute the average median level of assessment upon which the 1983 multiplier was based. Similarly, the average median level of assessment for the 1984 multiplier was calculated on the basis of 1981, 1982, and 1983 sales ratio studies. In preparing each of the sales ratio studies, the Department compared assessments for the prior year to sales prices for the year of *535the study. For example, the 1980 sales ratio study had 1979 property assessments in the numerator and the 1980 sales prices of those properties in the denominator. The Department then applied an adjustment factor to the median level of assessment calculated in each sales ratio study to take into account changes in assessment levels made by the county assessor or the board of appeals since the year of the assessments. In calculating the 1984 multiplier, for instance, the Department adjusted the median levels of assessment for each of the three studies used for changes in levels of assessment through the 1984 revisions. The Department did not attempt to determine actual changes in the assessments of the individual parcels used in the studies, but simply adjusted the overall median by the average increase in assessments after the data was collected.
The plaintiffs initially object that the Department’s sales ratio study methodology defies the statutory directive. They point to the language of section 146, which requires the Department to use in its sales ratio studies only assessments “as revised by ***[the] board[] of appeals.” (Ill. Rev. Stat. 1985, ch. 120, par. 627.) Similarly, section 148a (Ill. Rev. Stat. 1985, ch. 120, par. 629a) requires the Department, in certifying the percentage to be added to or deducted from the aggregate assessed valuation, to compare the estimated percentage to “the level of assessments of the assessed valuations as made by the assessors and thereafter finally revised by the board of review or board of appeals.” Plaintiffs’ contention is that these provisions, together with the requirement of section 1(20) that the level of assessment determined by the sales ratio studies must be “adjusted to take into account any changes in assessment levels since the data for such studies were collected,” require that the assessments used in the numerator of the sales ratio studies be finally revised assessments for the tax year *536for which the multiplier is being calculated. Thus, under plaintiffs’ submission, the sales ratio studies used in arriving at the 1983 multiplier would compare finally revised 1983 assessments with 1980, 1981, and 1982 sales prices, respectively. In contrast, the Department, as noted above, compared 1979 assessments to 1980 sales, 1980 assessments to 1981 sales and 1981 assessments to 1982 sales, and then adjusted the levels of assessments to reflect the average of changes made by the assessor and the board pf appeals through 1983. According to the plaintiffs, the Department’s methodology of using “old or imaginary” assessments results in a lower median level of assessment and thus a higher multiplier.
The starting point of our analysis is the well-established principle that courts must give substantial weight and deference to the interpretation placed on a statute by the agency charged with its administration and enforcement. (Gladstone Realtors v. Village of Bellwood (1979), 441 U.S. 91, 107, 60 L. Ed. 2d 66, 81, 99 S. Ct. 1601, 1612; Illinois Consolidated Telephone Co. v. Illinois Commerce Com. (1983), 95 Ill. 2d 142, 152; K. Davis, Administrative Law secs. 7:11 through 7:13 (2d ed. 1979).) Giving appropriate consideration to the Department’s interpretation, we disagree with the plaintiffs that the methodology employed by the Department violates the statutory directives.
None of the relevant provisions explicitly state which years’ assessments are to be utilized, but section 3 of the Real Estate Transfer Tax Act supports the Department’s methodology. That statute requires the assessor to insert on the green sheet completed for each property transfer “the most recent assessed value” of the property sold and to transmit “all such” green sheets to the Department on a monthly basis. Since assessments are apparently not finalized until the year following the assessment and the assessor is required to transmit the green *537sheets monthly, “the most recent assessed value” is that for the year preceding the sale. Thus, the legislature has apparently sanctioned the Department’s use of prior year assessments in performing its sales ratio studies.
Plaintiffs object that we cannot properly look beyond the contours of the Revenue Act of 1939 in ascertaining its meaning. Not only does this objection overlook the principle that related statutes should be construed in pari materia (Spring Hill Cemetery v. Ryan (1960), 20 Ill. 2d 608, 615; see People v. O’Donnell (1987), 116 Ill. 2d 517), it would ignore the explicit invitation to do so contained in the Real Estate Transfer Tax Act. As quoted above, section 3 of that Act expressly refers to section 1(20) of the Revenue Act. (Due to manifest drafting errors, this citation is actually to section 1(24) of “this Act.” Section 1(20) was formerly numbered 1(24) (see Pub. Act 83 — 121), and both the Revenue Act of 1939 and the Real Estate Transfer Tax Act were amended by Public Act 83 — 1063, effective March 1, 1984, which inserted the relevant cross-reference.) Moreover, the obvious purpose for requiring transmittal of green sheets containing assessment, sales and financing information to the Department is to provide data for the calculation of the multiplier. We are not persuaded that the provisions of the Revenue Act itself support the plaintiffs’ contention that the green sheets are to provide only “preliminary information.”
The plaintiffs also' rely on section 1(20), which requires the sales ratio studies be “adjusted to take into account any changes in assessment levels implemented since the data for such studies were collected.” (Emphasis added.) (Ill. Rev. Stat. 1985, ch. 120, par. 482(20).) Section 1(20), though, actually undercuts the plaintiffs’ position. That section obviously contemplates that the data used in the sales ratio studies will not be the brand-new data which the plaintiffs suggest is mandatory, but *538rather data which requires “adjustment.” Further, the Department is required only to take changes in assessment “levels” into account, and this is precisely what it does through its adjustment procedure. By contrast, plaintiffs want the Department, instead of adjusting levels of assessment, to actually compute new sales ratio studies using the new assessments of each specific property contained in the study. The plaintiffs’ view also seems to conflict with the legislative directive that the Department use “studies for the 3 most recent years preceding the assessment year.” We can discern no statutory authority for requiring the Department, which must equalize assessments in all 102 counties in the State, to undertake new studies each year based on the most recent assessment data for the properties to be analyzed.
Further buttressing the Department’s methodology are the standards of the International Association of Assessment Officials (IAAO), which provide that, the sales used in studies conducted for purposes of interjurisdictional equalization should be those occurring after the date of the assessment in order to “ensure the independence of assessed values and sales prices.” (IAAO, Standard on Assessment Ratio Studies 3.6.2.1 (1980).) The Department's hearing officer, who supervises calculation of the multipliers, stated that using assessments that follow the sale creates a significant bias in the study. The plaintiffs do not contradict that conclusion; indeed, they concede that “sales chasing” is generally disapproved, but simply maintain that it is within the legislature’s prerogative to vary from the IAAO standards. While the legislature could require a procedure inconsistent with the IAAO standards, without clearer guidance we will not presume that it actually has ordered the Department to flout generally accepted equalization principles.
*539The plaintiffs’ final argument on this point is that the Department formerly utilized the very methodology the plaintiffs are now advocating. (See Commonwealth Edison Co. v. Property Tax Appeal Board (1984), 102 Ill. 2d 443, 451.) The Revenue Act of 1939 does not, however, tie the Department for all time to a methodology which it determines to be unwise or unworkable. In addition to finding that the accuracy of the study proposed by the plaintiffs would be impaired by the use of biased assessments and loss of parcels whose classification had changed since the sale, the hearing officer concluded that, as a practical matter, awaiting the current-year assessments would delay issuance of the multiplier by several months. No evidence was introduced by the plaintiffs to contradict that finding.
The Department’s interpretation of the relevant statutes appears to us to be a reasonable one. The provisions are ambiguous, and the plaintiffs can hardly argue that only one construction of the statute is plausible since their objections filed with the Department and their complaints for administrative review urged yet a third interpretation. In those documents the plaintiffs argued that sales ratio studies should compare, for example, 1981 assessments to • 1981 sales prices. We decline to overrule the Department’s judgment on how the statutes are to be applied.
The plaintiffs next contend that the Department’s failure to use property appraisals in addition to property transfers violates section 146 of the Revenue Act as well as accepted assessment standards. As quoted above, section 146 requires the Department to ascertain the median level of assessment through “analysis of property transfers, property appraisals, and such other means as it deems proper and reasonable.’’ In response to the plaintiffs’ administrative objections, the Department’s hearing officer stated that appraisals were not used for *540Cook County because an adequate number of sales was available.
Plaintiffs argue that while the use of “other means” is discretionary with the Department, the statute commands the use of both property appraisals and property transfers. In People ex rel. Wenzel v. Chicago & North Western Ry. Co. (1963), 28 Ill. 2d 205, this court was faced with a contention that studies using only transfers and not appraisals should be inadmissible. Interpreting the very statutory language at issue here, the court determined that the statute required only that the Department “use such means as it deems ‘proper and reasonable.’ ” (28 Ill. 2d 205, 216.) While the duty to equalize is itself mandatory (Hamer v. Lehnhausen (1975), 60 Ill. 2d 400), it does not follow that every word in the Revenue Act of 1939 concerning equalization is likewise mandatory. As this court stated in Andrews v. Foxworthy (1978), 71 Ill. 2d 13, 21, a statutory provision is generally directory if it “merely directs a manner of conduct for the guidance of the officials.” The direction to use property appraisals is plainly such a guideline. This conclusion is supported by the discretion granted generally to the Department in determining the multiplier: section 148a of the Act (Ill. Rev. Stat. 1985, ch. 120, par. 629a) provides in part that the multiplier certified shall “represent the considered judgment” of the Department. The IAAO standards concerning appraisals do not require the use of appraisals or furnish any reason to believe the legislature commanded their use. Although expert evidence was presented at the 1984 multiplier hearing recommending the use of an appraisal method, the Department was free to reject that recommendation, which was based on a report that was not final and did not include data supporting its conclusions.
The plaintiffs also say that the Department’s sales ratio studies violate both the statute and accepted statisti*541cal principles in: (a) failing to make deductions from sales prices to take into account instances of so-called creative financing, and (b) failing to deduct or verify deductions for the value of personal property included in real property transfers.
Section 1(20) of the Revenue Act of 1939 now requires the Department to take into account the effects of creative financing, and section 3 of the Real Estate Transfer Tax Act provides a source for the necessary information. The statutory requirement for taking creative financing into account became effective January 1, 1983 (see Pub. Act 82 — 931), and was substantially amended effective March 1, 1984 (see Pub. Act 83 — 1063). Prior to January 1, 1983, the Real Estate Transfer Tax Act did not require the green sheets to contain questions on creative-financing. It is undisputed that the Department actually did make the required adjustments for the 1983 sales ratio study in calculating the 1984 multiplier. The Department made no such adjustments for any of the studies used in computing the 1983 multiplier, and it did not adjust the 1981 or 1982 studies in computing the 1984 multiplier. Neither the plaintiffs nor the Department presented any evidence as to the availability of financing data for years prior to 1983 or the difficulty in attempting to apply such adjustments retroactively. At the 1983 multiplier hearing, the hearing officer noted that no evidence was presented suggesting that a different level of assessment would result if creative financing had been taken into account. In the absence of such evidence or any clear legislative mandate that earlier sales ratio studies should be recomputed to reflect adjustments for creative financing, we find no error in the Department’s procedure.
The Department agrees that it is required to deduct the value of any personal property involved in a transfer of real estate before using the sales price in its sales ra*542tio study. (Ill. Rev. Stat. 1985, ch. 120, par. 482(20).) The hearing officer stated that the value of personal property was deducted from sales used in the 1981, 1982 and 1983 studies, and that assertion is not contradicted by anything in the record. (Although the plaintiffs have not made a point of it, the record does not reveal whether personal property was deducted from sales prices in the 1980 study.) The plaintiffs maintain, however, that the Department only deducts the value of personal property which is reported on the green sheets, and does not attempt to verify those declarations. As the hearing officer responded in her report on the 1984 multiplier, the accuracy of the personal property deductions reported on the green sheets is ensured by the fact that failure to report the full value of personal property will result in a higher real estate transfer tax for the taxpayer. The statute also makes it a Class B misdemeanor to wilfully falsify. or omit any information required on the green sheet (Ill. Rev. Stat. 1985, ch. 120, par. 1005), and the green sheet form itself carriés a warning to that effect. The relevant statutory provisions provide a data source — the green sheets — for the deductions, and while verification of this information might be preferable, the statutes do not require it. Further confirmation could also be extremely burdensome on the Department.
The plaintiffs also suggest in passing that the Department’s editing is in other respects insufficient. Again, the record does not support this argument. At the 1984 multiplier hearing, the Cook County assessor objected to the inclusion of 527 parcels in the sales ratio studies. Of these, 243 had already been discarded by the Department and another 92 were excluded on the assessor’s objection; the hearing officer found the rest of the challenges unsupported or meritless. After making the additional exclusions, the Department retabulated the *543sales ratio studies, but the editing did not result in any change in the multiplier.
The next statistical challenge to the Department’s sales ratio studies concerns whether the properties analyzed in the various classes are “representative” of all property in those classes. The plaintiffs correctly note that a sales ratio study draws, from the assessment level of a sample of properties, an inference as to the actual median level of assessment of all property in the county, and that representativeness is important to the validity of the study (see In re Application of Rosewell (1985), 106 Ill. 2d 311, 320-21). According to the plaintiffs, the Department’s failure to “stratify” its sample properties adequately renders the studies unrepresentative and statistically invalid.
It is undisputed that the Department does stratify, that is, separately analyze, data for each of the five major classifications of property defined in the Cook County Real Property Assessment Classification Ordinance and for subclass 5-93 (industrial properties) of the residual category Class 5. Plaintiffs argue, however, that since Class 3 (residential property containing seven or more units) and Class 5 are not further stratified by subclass, the studies cannot be considered indicative of the true levels of assessment. In support, the plaintiffs point out that subclass 5-17 — a category of commercial one-story stores — constitutes almost 50% by number of the Class 5 samples, but only 9 to 10% of the valuation of all Class 5 properties, and is thus highly overrepresented in the Class 5 study.
The Department responds that further stratification is unnecessary and would lead to reduced sample sizes, which would in turn reduce statistical confidence in the study. With respect to Class 5-17, the Department argues that the proper comparison is between its presence in the sample and its proportion by parcel count (as op*544posed to value) in the population, which is 37%. The Department’s hearing officer found that additional stratification would be impractical because the descriptions of the subclasses are brief, fragmentary and overlapping, making it difficult to determine into which subclass a particular property should be placed or to catch mistakes in classification. She also found no evidence that further stratification would result in a different median level of assessment from the Department’s studies. The hearing officer noted that when the Department stratified by assessment district and by five classes for 1982 sales, giving 20 well-defined strata, the additional stratification made a difference of only 0.01% in the county weighted median level of assessment.
We believe that the decision on how to stratify its sales ratio studies is properly committed to the Department’s discretion. We are not persuaded that the Department’s calculations resulted in statistically invalid sales ratio studies.
Finally, the plaintiffs urge that the sales ratio studies upon which the multipliers are based are “statistically meaningless,” as evidenced by the high coefficients of dispersion for some classes of property in Cook County. Plaintiffs cite a statement by this court in In re Application of Rosewell (1985), 106 Ill. 2d 311, 321, concerning defects of the studies used there: “Besides lacking randomness, representativeness, and sufficient editing, the coefficients of dispersion are too high for the median assessment levels to have statistical significance relative to the standard of proof.”
Rosewell was a tax objection proceeding in which the objector attempted to use sales ratio studies to prove that other properties were underassessed relative to the objector’s property. In such cases the objector must prove actual or constructive fraud by clear and convincing evidence (106 Ill. 2d 311, 318), and this court only *545concluded that based on largely uncontradicted expert testimony, the studies did not furnish such compelling evidence. In this case, the Department does not have to produce clear and convincing evidence justifying the multiplier; in fact, the burden of proof is on the plaintiffs. This case also differs from Rosewell because the plaintiffs have not demonstrated that flaws in the studies produced high coefficients of dispersion. Further, the Department, which was not a party to the Rosewell case, maintains that coefficients of dispersion do not measure the reliability of a sales ratio study, but only variability of assessments. (See IAAO Standard 2.2.) According to the Department, a high coefficient of dispersion is undesirable because it indicates that taxpayers are not being treated equally with respect to assessment, but does not show that a sales ratio study is inaccurate to prove the median level of assessment. Plaintiffs concede that a high coefficient of dispersion may indicate nonuniformity in assessment, a deficiency irrelevant to the issue presented here. Unlike in Rosewell, there was no expert testimony below on the import of the coefficient of dispersion, and we are unwilling to resolve this controversy based on expert testimony which was briefly summarized in the Rosewell opinion but which has not been shown by the plaintiffs to be relevant to this case. (See People v. Emrich (1986), 113 Ill. 2d 343, 352-53.) We conclude that the coefficients of dispersion revealed by the Department’s calculations do not, on this record, demonstrate that the sales ratio studies are statistically flawed.
For the reasons stated, the judgmént of the circuit court of Cook County, affirming the Department’s determinations for the tax years 1983 and 1984, is affirmed.
Judgment affirmed.
JUSTICE GOLDENHERSH took no part in the consideration or decision of this case.