Whenever you use statistical averages to speak about individuals, you run the risk of obscuring more than you reveal. When the data is all over the place, the average can be a meaningless number, and even when there is a normal distribution the outliers may violate all your conclusions.
When it comes to human psychology, things are even worse. This new study found that not only did the averaging statistics hide a lot of variation between individuals, it also masked a lot of variation within individuals, that is, in how they tested from one day to the next.
This study was about depression and anxiety, and it was supposed to measure things like how strongly the two are correlated. What it found was that the standard deviation for individuals, from one day to the next, was eight times greater than the standard deviation for the data set as a whole.
The mean values may still be useful for something, but doing those statistics actually obscures the most fascinating finding of the study, which is about variation: not only do our moods vary a lot, but the correlations between different parts of our moods vary a lot, too. For example, the study tried to determine if brooding is correlated with depression, and the answer was that if you average the data from all 1043 participants, yes, but for you it will depend on what day it is.
For describing human societies, averages are essential, but for getting to know any particular person they are worse than useless. Even the average of one person's behavior may not tell you anything about how he or she will act on any given day.