A critical issue in addressing medical conditions is measurement. Memory measurement is difficult, especially episodic memory, which is disrupted by many conditions. On-line computer testing can precisely measure and assess several memory functions. This study analyzed memory performances from a large group of anonymous, on-line participants using a continuous recognition task (CRT) implemented at https://memtrax.com. These analyses estimated ranges of acceptable performance and average response time (RT). For 344,165 presumed unique individuals completing the CRT a total of 602,272 times, data were stored on a server, including each correct response (HIT), Correct Rejection, and RT to the thousandth of a second. Responses were analyzed, distributions and relationships of these parameters were ascertained, and mean RTs were determined for each participant across the population. From 322,996 valid first tests, analysis of correctness showed that 63% of these tests achieved at least 45 correct (90%), 92% scored at or above 40 correct (80%), and 3% scored 35 correct (70%) or less. The distribution of RTs was skewed with 1% faster than 0.62 s, a median at 0.890 s, and 1% slower than 1.57 s. The RT distribution was best explained by a novel model, the reverse-exponential (RevEx) function. Increased RT speed was most closely associated with increased HIT accuracy. The MemTrax on-line memory test readily provides valid and reliable metrics for assessing individual episodic memory function that could have practical clinical utility for precise assessment of memory dysfunction in many conditions, including improvement or deterioration over time.