Which measure indicates distances from the mean in the normal distribution in units of standard deviations?

Which measure indicates distances from the mean in the normal distribution in units of standard deviations?

• A. Standard deviation
• B. Z-score
• C. Inter-quartile range
• D. Present value

Answer: (B)

Distances from the mean expressed in units of standard deviations are captured by the z-score. It standardizes a value by subtracting the mean and dividing by the standard deviation, giving a dimensionless measure of how far the value is from the mean in terms of standard deviation units. In a normal distribution, this corresponds to the standard normal distribution with mean 0 and standard deviation 1, so you can compare scores from different distributions and look up probabilities directly. The standard deviation is the spread in original units, the inter-quartile range measures the spread of the middle 50%, and present value isn’t a relevant statistical measure here.

Distances from the mean expressed in units of standard deviations are captured by the z-score. It standardizes a value by subtracting the mean and dividing by the standard deviation, giving a dimensionless measure of how far the value is from the mean in terms of standard deviation units. In a normal distribution, this corresponds to the standard normal distribution with mean 0 and standard deviation 1, so you can compare scores from different distributions and look up probabilities directly. The standard deviation is the spread in original units, the inter-quartile range measures the spread of the middle 50%, and present value isn’t a relevant statistical measure here.