Eleven companies that own and lease railroad cars to operating carriers (the “Carlines”) appeal a district court decision 561 F.Supp. 595 which upheld' the State of Arizona in an action challenging Arizona’s assessment of ad valorem taxes. We affirm.

The Carlines and Arizona agree that 49 U.S.C. § 11503 (b)(1) forbids assessing Car-lines’ property at an assessment ratio exceeding the “average assessment ratio” applicable to all “other commercial and industrial property in the assessment jurisdiction.” They disagree about what this language means.

The Carlines’ first claim is that the state ought to include in its calculation of commercial property all the business inventories in the state (which are categorically exempt from ad valorem taxes) in determining the assessment ratio. This claim has nothing to commend it but a careful lawyer’s desire to leave no possible theory unexplored. We find no authority requiring untaxed property to be included in an average of assessed value for taxed property.

The Carlines’ next contention is that leased residential property must be considered “commercial and industrial” property for the purposes of § 11503(b)(1). This contention fails because nothing in the statute prohibits Arizona from treating property devoted to residential use differently from property devoted to commercial and industrial use. See 49 U.S.C. § 11503 (a)(4).

The Carlines’ third claim is that Arizona’s assessment ratio discriminates against them compared to the assessment ratios of other taxpayers. It asks this court for a rule requiring the state to employ a “median” rather than “weighted mean” formula in determining the assessment ratio applicable to rail transportation property.

Arizona law divides real and personal property into eight assessment categories. A.R.S. § 42-136. Classes one, two and seven represent substantial value and relatively few taxpayers. These classes are assessed centrally by the state. The remaining five classes are assessed locally by each county. The property in each category is assessed at a statutorily-fixed percentage of its full cash or limited property value, whichever is applicable. The statutory assessment scheme can be summarized for the relevant years as follows:

The Carlines have the burden of proving that the weighted mean assessment ratio is discriminatory when compared to the assessment ratios of other taxpayers. See Clinchfield R. Co. v. Lynch, 700 F.2d 126, 131-2 (4th Cir.1983). This burden is not satisfied by simply finding fault with the “weighted mean” as compared to the Carlines’ preferred “median.” Although the Carlines put on testimony tending to prove that if a “median” system were used their taxes would be substantially lower, they did not prove that under Arizona’s system their taxes were within the forbidden zone of discrimination.

The Carlines have seized upon some language in Clinchfield R. Co. v. Lynch, 527 F.Supp. 784, 789 (E.D.N.C.1981), saying that the “median” approach was the correct method of striking an average in that case. Neither the district court memorandum nor the Fourth Circuit opinion affirming, however, indicated that the “median” approach is the only one that will comply with § 11503. Clinchfield R. Co. v. Lynch, 700 F.2d 126 . We are likewise unpersuaded by the Carlines’ self-serving argument that the “sales assessment ratio studies” referred to in the legislative history of § 11503 requires the “median” approach to the exclusion of all others.

Congress itself did not have any misconception regarding sales assessment ratio studies. A committee report appendix attached unchanged to successive versions of the bill explained the term “sales ratio assessment study.” This appendix is quoted in part by our court in State of Ariz. v. Atchison, T. & S.F. R. Co., 656 F.2d 398, 404 (9th Cir.1981). In describing the methodology of a sales assessment ratio study, the legislators referred to a “weighted average” —i.e., the (b)(1) approach — rather than a median:

Accord S.Rep. No. 91-630, 91st Cong., 1st Sess. 26-27 (1969).

The Carlines have failed to show that the statute requires the median approach. Moreover, the median approach would ignore legitimate classifications which are fundamental to Arizona’s tax system. The Carlines have failed to carry their burden of proving that use of the weighted mean assessment ration is discriminatory.

Affirmed.

. The Carlines’ property is in class 7. Under A.R.S. § 42-227.B.7(a) and (b), the assessment ratio applicable to rail transportation property is a “weighted mean” computed by dividing the total assessed valuation of Class 1, 2 and 3 property by the total taxable value of that property. Arizona contends that it enacted this assessment ratio for the express purpose of adopting the federal formula.