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.

View Explanation

Log in for full answers

Similar Questions

Question at position 42 A standard score describesHow far a particular score is from the medianHow far apart the mean and median of a distribution areHow much skew there is in a distributionHow much spread there is in a distributionHow far a particular score is from the mean

A Z-score tells us:

The critical value z.05 is the .95-quantile for a standard normal distribution. Compute z.05.

Question at position 1 What determines how far a particular value is from the mean relative to the data set’s standard deviation?Coefficient of variationz-scorePercentilVarianceClear my selection

When measuring arrival times for class, we can use a specific measurement of any given late student to best determine:

When measuring arrival times for class, we can use a specific measurement of any given late student to best determine:

Let x be an observation from a Normal Distribution with mean µ and standard deviation σ. The standardized score (z-score) is defined byz = (x – µ)/σFor the following values of x, µ and σ, find z. Give your answer correct to 2 decimal places.x = 112 µ = 100 σ = 12.5

This is the formula for [ Select ] Pearson’s r correlation z-test for a sample mean z-test for an individual score effect size .

More Practical Tools for International Students

Exam Browser Assistant

Stylized Writing Assistant

Plagiarism Checker Assistant

Citation Assistant

In-Class Translation Assistant

Class Notes Assistant

Quiz Search Assistant

Past Exam Questions by School

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler