Which statement about z-score transformation is true?

Which statement about z-score transformation is true?

• A. It changes the shape of the distribution.
• B. It leaves the units unchanged.
• C. It does not standardize data.
• D. It standardizes data so that the transformed distribution has a mean of 0 and a standard deviation of 1.

Answer: (D)

Z-score transformation standardizes data by expressing each value as how many standard deviations it is from the mean. For each observation, you subtract the mean and divide by the standard deviation. This re-scaling makes the transformed distribution have a mean of zero and a standard deviation of one, while the shape of the distribution stays the same because you’re only shifting and rescaling, not altering skewness or tails. As a result, the units disappear and the scores become dimensionless. If the original data are normally distributed, the z-scores follow a standard normal distribution with mean 0 and SD 1. This method is especially useful for comparing values across different scales or identifying outliers.

Z-score transformation standardizes data by expressing each value as how many standard deviations it is from the mean. For each observation, you subtract the mean and divide by the standard deviation. This re-scaling makes the transformed distribution have a mean of zero and a standard deviation of one, while the shape of the distribution stays the same because you’re only shifting and rescaling, not altering skewness or tails. As a result, the units disappear and the scores become dimensionless. If the original data are normally distributed, the z-scores follow a standard normal distribution with mean 0 and SD 1. This method is especially useful for comparing values across different scales or identifying outliers.