Generally, data gathered from natural phenomena obeys normal distribution, I think your data should obey the normal distribution as well. The more you have data the better you may do estimation or prediction.
In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
There are many methods to do the test.
Simple back-of-the-envelope test takes the sample maximum and minimum and computes their z-score, or more properly t-statistic (number of sample standard deviations that a sample is above or below the sample mean), and compares it to the 68–95–99.7 rule: if one has a 3σ event (properly, a 3s event) and substantially fewer than 300 samples, or a 4s event and substantially fewer than 15,000 samples, then a normal distribution will understate the maximum magnitude of deviations in the sample data.
But if your sample data is fixed ( I mean does not change with time) then you can precompute necessary statistics and later compare and draw conclusion in $O(1)$ time. But I would update my sample data once a day or hour, and then check it visually (for example you may detect outliers) and recompute statistics on a regular base.