I think you missed something in the text as we CAN actually find out the members of the set.
We know that they are consecutive even integers and the mean is 382. That means there are 19 consecutive even integers on the left of this number and another 19 on the right (39 - 1 = 38) and 38/2 = 19.
However in this case, you don't really need to know the actual members of the set since the standard deviation would be known by default regardless of the number values (2, 4, 6, etc) or (20224, 20226, etc). We know that they are spaced within 39*2 = 78 of each other and that's all we need to know. We don't need to calculate the details.
Hope this helps.
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