ARBITRON INC. WAIVER AND AMENDMENT OF EXECUTIVE RETENTION AGREEMENT

Exhibit 10.58

ARBITRON INC.

WAIVER AND AMENDMENT OF

EXECUTIVE RETENTION AGREEMENT

This is an agreement (the “Agreement”) between Arbitron Inc. (the “Company”) and Debra Delman (“you”), dated as of December 17, 2012. Except as otherwise defined herein, capitalized terms used in this Agreement have the same definition as in the Executive Retention Agreement between you and the Company, dated as of August 27, 2012 (the “Retention Agreement”).

WHEREAS, you and the Company have previously entered into the Retention Agreement; and

WHEREAS, you and the Company desire to amend the Retention Agreement.

THEREFORE, you and the Company agree as follows, in consideration of the services to be received from you and the ongoing compensation to which you will be entitled and other good and valuable consideration, the receipt and sufficiency of which the parties hereby acknowledge:

(1) The first recital (WHEREAS paragraph) of the Retention Agreement is revised by striking “August 25, 2013” and replacing it with the date that is the second anniversary of the date hereof.

(2) Section 2(b)(i) is amended to delete “ pay you an amount in cash equal to 12 times your Reference Compensation (as defined below) as in effect immediately before the termination (or, if the Position Diminishment relates to a reduction in base salary, before such reduction)” and replace it with “pay you an amount in cash equal to the sum of (x) 12 times your monthly base salary as in effect immediately before the termination (or, if the Position Diminishment relates to a reduction in base salary, before such reduction) and (y) your target annual bonus for the year of termination”.

(3) Section 2(c) is amended to delete “24 months of Reference Compensation” and replace it with “24 months of your monthly base salary and 2 times your target annual bonus for the year of termination”.

(4) Section 2(g)(iv) is deleted in its entirety.

(5) The text of Exhibit A is deleted and replaced in its entirety by the following:

“The Company will make the payments under this Agreement without regard to whether the deductibility of such payments (or any other payments or benefits) would be limited or precluded by Section 280G of the Internal Revenue Code of 1986, as amended (the “Code”) and without regard to whether such payments would subject you to the federal excise tax levied on certain “excess parachute payments” under Section 4999 of the Code; provided, however, that if the Total After-Tax Payments (as defined below) would be increased by the reduction or elimination of any payment and/or other

benefit (including the vesting of your equity awards) under this Agreement (the “Parachute Payments”), then the amounts payable under this Agreement will be reduced or eliminated by determining the Parachute Payment Ratio (as defined below) for each Parachute Payment and then reducing the Parachute Payments in order beginning with the Parachute Payment with the highest Parachute Payment Ratio. For Parachute Payments with the same Parachute Payment Ratio, such payments shall be reduced based on the time of payment of such Parachute Payments, with amounts having later payment dates being reduced first. For Parachute Payments with the same Parachute Payment Ratio and the same time of payment, such Parachute Payments shall be reduced on a pro rata basis (but not below zero) prior to reducing Parachute Payments with a lower Parachute Payment Ratio. For purposes hereof, the term “Parachute Payment Ratio” shall mean a fraction, the numerator of which is the value of the applicable payment for purposes of Section 280G of the Code, and the denominator of which is the intrinsic value of such Parachute Payment. The Company’s independent, certified public accounting firm (the “Accountants”) will determine whether and to what extent Parachute Payments under this Agreement are required to be reduced in accordance with this paragraph. Such determination by the Accountants shall be conclusive and binding upon you and the Company for all purposes. For purposes of making the calculations required by this paragraph, the Accountants may make reasonable assumptions and approximations concerning applicable taxes and may rely on reasonable, good faith interpretations concerning the application of Section 280G and 4999 of the Code. You and the Company shall furnish to the Accountants such information and documents as the Accountants may reasonably request in order to make a determination under this paragraph. The Company shall bear all costs the Accountants may reasonably incur in connection with any calculations contemplated by this paragraph. If there is an underpayment or overpayment under this Agreement (as determined after the application of this paragraph), the amount of such underpayment or overpayment will be immediately paid to you or refunded by you, as the case may be, with interest at the applicable federal rate provided for in Section 7872(f)(2) of the Code. For purposes of this Agreement, “Total After-Tax Payments” means the total economic value of all “parachute payments” (as that term is defined in Section 280G(b)(2) of the Code) made to or for the benefit of you (whether made under the Agreement or otherwise), after reduction for all applicable federal taxes (including, without limitation, the tax described in Section 4999 of the Code), and present valued using the discount rate applicable under Section 280G of the Code.”

(6) All other provisions of the Retention Agreement remain in effect as written.

Signatures on Page Following

IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the day and year first set forth above.