Alocal garden club had 14 members with a mean age of 34. then two new members joined. one was 24 years old, and the other was 36 years old. how did the mean age change after they joined? the mean age increased. the mean age decreased. it isn't possible to determine how the mean would change. the mean age stayed the same.

The mean age decreased.

I find it convenient to look at the additions with respect to the current mean age.

The current total age is 14×34. We have added members with ages (34 -10) and (34 +2), so the new total age is ...

... (34×14) + (34 -10) + (34 +2) = (16×34) - 8

Dividing this total by 16 will give the new mean age. (We already know it is less than 34.)

... ((16×34) -8)/16 = 34 - 1/2 = 33 1/2 . . . new mean age; a decrease

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