Four students found the mean of the data set 26, 31, 39, 30, 16, 16, 18, 38. Which student found the correct mean?
2 answers:
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The set is linearly dependent.
To explicitly prove this, we need to show there is at least one choice of constants such that
or equivalently,
which is the same as solving the system of equations
From the first and last equations, we have and
. Substituting these into the second equation leaves us with
, and so the overall solution set is
for which there are infinitely many not-all-zero solutions.