Question

Determine whether the following statement is true of false. If the statement is​ false, make the necessary​ change(s) to produce a true statement.
The sum of the deviations from the mean for a data set is always zero.
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Part 1
Choose the correct answer below.
A.
The statement is false because the sum of the deviations from the mean for a data set is zero only when the mean of the data set is zero.
B.
The statement is true.
C.
The statement is false because the sum of the deviations from the mean for a data set is always positive.
D.
The statement is false because the sum of the deviations from the mean for a data set is always negative.

Answer 1

B. The statement is true.

Reason: If x̄ = (1/n)∑xi, then ∑(xi − x̄) = ∑xi − n x̄ = ∑xi − n(∑xi/n) = 0.