4. The mobile terminal according to claim 1 , wherein the conversion database stores frequency-of-use information indicating frequency of previous use of converted data items, the character conversion unit updates the frequency-of-use information according to confirmation of one of the plurality of conversion candidates as the converted data item, and in a case where each of conversion candidates searched out by the data search unit includes a character which immediately follows the one or more already inputted characters and total number of times the character input key is to be pressed down before inputting the character is identical to each other in the searched out conversion candidates, the display-order setting unit determines the order of display of the searched out conversion candidates so that the total number of times one of the one or more select keys is to be pressed down before selecting each of the searched out conversion candidates decreases with increase in frequency of previous use of the searched out conversion candidates.
4. The mobile terminal according to claim 1 , wherein the conversion database stores frequency-of-use information indicating frequency of previous use of converted data items, the character conversion unit updates the frequency-of-use information according to confirmation of one of the plurality of conversion candidates as the converted data item, and in a case where each of conversion candidates searched out by the data search unit includes a character which immediately follows the one or more already inputted characters and total number of times the character input key is to be pressed down before inputting the character is identical to each other in the searched out conversion candidates, the display-order setting unit determines the order of display of the searched out conversion candidates so that the total number of times one of the one or more select keys is to be pressed down before selecting each of the searched out conversion candidates decreases with increase in frequency of previous use of the searched out conversion candidates. 5. The mobile terminal according to claim 4 , wherein the display control unit makes the display device concurrently display a first image and a second image, where a part of the plurality of conversion candidates are displayed in the first image in order of frequency of use on the basis of the frequency-of-use information, and a rest of the plurality of conversion candidates are displayed in the second image in the order of display of the plurality of conversion candidates determined by the display-order setting unit.