Which statement is true about standardizing data with z-scores?

Which statement is true about standardizing data with z-scores?

• A. It always requires the data to be normally distributed.
• B. It changes the relative order of data values.
• C. It produces a distribution with mean 0 and SD 1.
• D. It makes all values positive.

Answer: (C)

Standardizing with z-scores centers the data around the mean and rescales by the standard deviation. This produces a distribution with mean 0 and standard deviation 1, which lets you compare values from different scales. The operation is a shift and a scale by a positive constant, so the relative order of values is preserved. It does not require normal distribution, and z-scores can be negative for values below the mean and positive for those above.

Standardizing with z-scores centers the data around the mean and rescales by the standard deviation. This produces a distribution with mean 0 and standard deviation 1, which lets you compare values from different scales. The operation is a shift and a scale by a positive constant, so the relative order of values is preserved. It does not require normal distribution, and z-scores can be negative for values below the mean and positive for those above.