A set of data with 100 observations has a mean of 267. There are six outliners in the data set, which have a mean of 688 if the six outliners are removed, what is the mean of the new data set?

272.04

Step-by-step explanation:

We must make a weighted average, as follows:

Each mean will have its weight, which would be the number of observations, therefore, the initial mean has a weight of 100.

And the final mean that we do not know its value but if its 94 (100 - 6) and the other mean that it is 688 and its weight is 6, we have the following equality:

100 * 297 = 688 * 6 + 94 * x

x would be the final mean, solving:

x = (29700 - 4128) / 94

x = 272.04

average after removing those 6 is 272.04