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 mean unchanged.
• C. It transforms data so that the mean is 0 and the standard deviation is 1.
• D. It cannot be applied to non-normal data.

Answer: (C)

Z-score transformation standardizes data by centering and scaling: for each value you subtract the mean and divide by the standard deviation, z = (x − μ)/σ. This process shifts the data so the mean becomes 0 and rescales it so the standard deviation becomes 1, putting all values in units of standard deviations from the mean. Because it’s a linear transformation, it doesn’t change the relative ordering or the shape of the distribution—the same spread pattern is preserved, just on a different scale. The mean is not left at its original value after standardization; it becomes zero. And you can apply this to any dataset with a computable mean and standard deviation, not only normal data. So the statement that’s true is that the transformation results in a mean of 0 and a standard deviation of 1.

Z-score transformation standardizes data by centering and scaling: for each value you subtract the mean and divide by the standard deviation, z = (x − μ)/σ. This process shifts the data so the mean becomes 0 and rescales it so the standard deviation becomes 1, putting all values in units of standard deviations from the mean. Because it’s a linear transformation, it doesn’t change the relative ordering or the shape of the distribution—the same spread pattern is preserved, just on a different scale. The mean is not left at its original value after standardization; it becomes zero. And you can apply this to any dataset with a computable mean and standard deviation, not only normal data. So the statement that’s true is that the transformation results in a mean of 0 and a standard deviation of 1.