1. An image data processing apparatus, comprising: a processor; and memory storing computer-readable instructions that, when executed, cause the processor to perform the following: execute a predetermined data processing of first image data; determine an actual loaded amount of recording media in a single discharge tray; identify an attribute of the first image data from among a plurality of attributes of image data; set a maximum loaded amount of recording media in the single discharge tray, up to which further discharge of recording media to the discharge tray is permissible, to a first specified value if the attribute of the first image data is a first attribute, and set the maximum loaded amount to a second specified value that is smaller than the first specified value if the attribute of the first image data is a second attribute different from the first attribute; determine, before executing the data processing, whether a predicted loaded amount of the recording medium loaded in the single discharge tray is in a first state or in a second state, the first state indicating that the loaded amount of the recording medium loaded in the single discharge tray is predicted not to be equal to or greater than the maximum loaded amount when the data processing is executed based on the first image data, and the second state indicating that the loaded amount of the recording medium loaded in the single discharge tray is predicted to be equal to or greater than the maximum loaded amount when the data processing is executed based on the first image data; cause removal of recording medium from the single discharge tray if it is determined that the predicted loaded amount of the recording medium loaded in the single discharge tray is in the second state; determine whether or not to start the data processing based on the first image data when it is determined that the predicted loaded amount of the recording medium loaded in the single discharge tray is in the second state; execute the data processing based on the first image data when the actual loaded amount is smaller than the maximum loaded amount and it is determined that the predicted loaded amount of the recording medium loaded in the single discharge tray is in the first state, execute the data processing based on the first image data until the actual loaded amount of the recording medium in the single discharge tray is equal to or larger than the maximum loaded amount, when the actual loaded amount is initially determined to be smaller than the maximum loaded amount, it is determined that the predicted loaded amount of the recording medium loaded in the single discharge tray is in the second state, and it is determined to start the data processing, and not to execute the data processing based on the first image data, when the actual loaded amount is smaller than the maximum loaded amount, it is determined that the predicted loaded amount of the recording medium loaded in the single discharge tray is in the second state, and it is determined not to start the data processing, or when the actual loaded amount is equal to or greater than the maximum loaded amount; wherein the data processing includes a process that causes forming of an image on a recording medium based on the first image data and further causes discharging, to the discharge tray, the recording medium on which the image has been formed, and the memory further stores instructions that, when executed, cause discharging, to the single discharge tray, a recording medium on which an image has been formed based on image data having a different attribute selected from the plurality of attributes of image data.