Thread: final score (X) when given SD, M, and variation

Hi,

Wondering how you would go about figuring the following problem.

N = 10, M = 20, SD = 2

Nine of the raw scores have a variation of +12, given the rest of the info on the sample, what is the tenth raw score?

Thank You

Four possible answers were given: 18, 12, 6, 2.

Also, what is meant by the 9 variation scores adding up to +12 is for example.

22 - 20 = 2
18 - 20 = -2
17 - 20 = -3
23 - 20 = 3

etc., and the total of X-M for the 9 raw scores was +12

Is this question even possible to figure out? Wouldn't you need at least the Sum of Squares for the 9 raw scores?

*the sum of deviation scores for the 9 raw scores = +12

If the question did not mention the SD and simply asked what the tenth score is if the sum of deviation scores for the other 9 = +12 then the answer would be 8, because (X-M=deviation score) so (8-20=-12) and all deviation scores add up to 0. I'm thinking the question is not possible, because if you use 8 as the tenth raw score then that results in a squared deviation of 144 (-12 x -12) which by itself is too great to produce a small SD=2. ??