The Z score of a value can never be negative.

Question

BlackTom AI · Accepted Answer

Consider the statement in question: whether the Z score of a value can ever be negative.
Option 1: True. If we interpret the claim as “the Z score can never be negative,” this would imply that all standardized deviations are nonnegative. In standard normal distribution terminology, Z scores measure how many standard deviations a value is from the mean, and they can lie below the mean, yielding negative standardized values. Therefore, claiming that a Z score cannot be negative contradicts the fundamental definition of Z as (value - mean) divided by standard deviation. Thus this option is incorrect.
Option 2: False. This aligns with the mathematical form of the Z score: Z = (X − μ) / σ. When X is less than the mean μ, the numerator is negative while σ is positive, resulting in a negative Z value. There is no restriction that Z must be nonnegative; negative Z scores indicate values below the mean. Hence this statement correctly describes the Z score behavior, making it the true assessment of the given claim.
In summary, the notion that Z scores cannot be negative is inconsistent with how standardization works, whereas recognizing that negative Z scores occur for values below the mean accurately reflects the concept. The negative Z values simply reflect positions on the left tail of the distribution relative to the mean.

COMM 291 Practice Quiz- Module 3

The Z score of a value can never be negative.

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