What is the formula for a z-score?

What is the formula for a z-score?

• A. (score-mean)/standard deviation
• B. (score+mean)/standard deviation
• C. (score-mean)*standard deviation
• D. (score/standard deviation) - mean

Answer: (A)

The z-score expresses how far a score is from the mean in units of standard deviation. To do this, you center the value by subtracting the mean, and then rescale by the distribution’s spread by dividing by the standard deviation. That is why the formula is (score minus mean) divided by standard deviation. The other forms don’t standardize correctly: adding the mean shifts the center, multiplying changes the scale inappropriately, and dividing then subtracting mixes steps in the wrong order, so it wouldn’t reflect standard deviation units.

The z-score expresses how far a score is from the mean in units of standard deviation. To do this, you center the value by subtracting the mean, and then rescale by the distribution’s spread by dividing by the standard deviation. That is why the formula is (score minus mean) divided by standard deviation. The other forms don’t standardize correctly: adding the mean shifts the center, multiplying changes the scale inappropriately, and dividing then subtracting mixes steps in the wrong order, so it wouldn’t reflect standard deviation units.