If you put into a bag 90 little balls of ivory, all of the same size, one sixth of them yellow, two sixths red, and three sixths black, and then draw them out one at a time at haphazard, there is no certainty that one colour will come out first rather than another, but there is probability in the proportions of one half for the black, one third for the red, and one sixth for the yellow. Whichever colour you happen to extract is always an irregularity, because that colour had not, so to speak, an entire right to come out, but only half a right, or a third, or a sixth part. But if, replacing the ball after each extraction, you go on repeating the same operation a very great number of times, you will find that the number of balls for each colour comes nearer and nearer to the relative proportions in respect of the colours. And the longer you continue, the more will the irregularity diminish, and the normal design become more apparent; thus clearly showing you, that the law which inclines the colours to regularize themselves, although accidentally disturbed in its action, would entirely prevail if you were to prolong the extractions to an indefinite length of time.
Agreeably to this, he who can only consider particular cases, is not in a position to be able to realize to himself the marvellous beauty of this universe; nay, in noticing the irregularities which are inevitable in it, he must take them as so many evidences of deformity; whereas he who considers a long series of events will see therein an admirably regular and symmetrical order.
In his example, if you look at a fine piece of embroidery, in which there is an immense amount going on, and you only look at a few threads, you will not see what is happening with the whole embroidery -- you will see a bit of color, then a bit of another color, and the like, and miss the whole picture to which each of the threads contributes.
The analogy is closer than it might appear. While we don't usually think of statistics as concerned with the beautiful, it is about the discovery of patterns and symmetries in a population, and thus connects directly to matters of beauty, which are also concerned with patterns and symmetries. If one can simply see the pattern or symmetry, one can perhaps simply see the beauty of something, but there are inevitably things whose full beauty is too big to catch at a glance, and in those cases the size and quality of your samplings can matter greatly, because fully seeing the beauty requires getting a sense of what is happening as a whole. But, of course, sampling alone is not enough, in statistical or aesthetic matters; one must have a way to make sense of the result.