A data set has a standard deviation of 4. If every value in the data set is multiplied by 3, what is the standard deviation of the new…

Standard deviation measures spread, so it scales with multiplication but does not change with addition. When every value is multiplied by 3, each distance from the mean is also tripled, so the standard deviation becomes $3 \times 4 = 12$, choice B. Choice A (4) would be correct if 3 were added to every value, which only shifts the data. Choice C (7) comes from adding 3 to the standard deviation. Choice D (64) comes from cubing 4; the variance would scale by $3^2 = 9$, giving 144, but the question asks for standard deviation. Multiplying by $k$ multiplies the standard deviation by $|k|$.