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The present invention claims priority from Japanese Patent Application No. 10-321378 filed Oct. 28, 1999, the contents of which are incorporated herein by reference. 1. Field of the Invention The present invention relates to a brain wave data processing device used for processing brain wave data to detect distinctive patterns, and more particularly to a brain wave data processing device which averages brain wave data in which distinguishing patterns are detected in individual brain wave data obtained in a single trial, and to a computer readable storage medium in which a program to realize this brain wave data processing device is loaded. 2. Description of Related Art When an excitation or event is added to a subject (trial), an electric potential evoked by the added excitation or event (evoked potential) would occur in the brain and spinal cord of the subject. In particular, a potential variation occurred in a cerebral cortex with a constant time relation to an excitation or event is referred to as an event-related potential (ERP). Such a potential or potential variation is generally observed as brain wave data, and used as effective data to know the mechanism of, for example, feeling, perception, and psychological phenomenon, or to find a position of an injury. However, the amplitude of the potential variations involved with the trial is considerably smaller than that of rhythmic, ordinary brain waves, so that a signal occurred from one observation is often indistinct. Therefore, a method has been devised in which multiple trials are performed under the same conditions and the brain wave data obtained from each trial are added and averaged with the time of excitation (event) as a reference point, causing components of the rhythmic, ordinary brain waves to be canceled, so that only the evoked potential obtained by the excitation (event) is extracted. This technique is referred to as an averaging method. Incidentally, as a technique to process an unsteady signal which changes over time to analyze whether or not a distinguishing component is included, in these days, attention has focused on the wavelet conversion. An example of the brain wave data subjected to the wavelet conversion in a single trial includes the reference xe2x80x9cP300 Single Trial Storage Processing Based on Wavelet Conversionxe2x80x9d by Masatoshi Nakamura, <PRESIDIO_ANONYMIZED_PERSON>, <PRESIDIO_ANONYMIZED_PERSON>, <PRESIDIO_ANONYMIZED_PERSON>, Yoshio Ikeda, and Hiroshi Shibasaki (Proceedings of the fifteenth SICE Kushu branch congress, pp. 355-358, Nov. 23, 1996). However, the device by Nakamura et al. provides only the wavelet conversion and inverse wavelet conversion with respect to the brain wave data, and includes only the filtering function to eliminate noises in live data. Further, although they have attempted to restrict parameters included in the wavelet conversion according to the result of filtering to the live data, the reliability of the result can not be expected, because they use a formula model as a true waveform. In addition, they have examined wavelet conversion parameters only in limited ranges, so that a considerable amount of information contained in the live data