You seem to be having trouble with the word "any." When their asking for "any constant," they don't mean "any one
", they mean "any possible
" constant. Thus, it doesn't matter if a set of numbers happens to work when you multiply it by one, unless it ALSO works with 2, pi, or 5,000,000. Therefore, since we have to have the same mean when multiplied by zero (in addition
to all those other big numbers), the average must be 0. II is not true because [-1, -1, -1, 3] is a valid set, and III isn't because os [0, 0, 0, 0,]
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