How is a z-score calculated?

How is a z-score calculated?

• A. The observation divided by the mean.
• B. The observation minus the mean divided by the standard deviation.
• C. The observation minus the median divided by the standard deviation.
• D. The mean divided by the standard deviation.

Answer: (B)

Calculating a z-score standardizes an observation by showing how far it is from the average in units of spread. You subtract the mean from the observed value and then divide by the standard deviation. This centers the data at zero and scales it so that one unit equals one standard deviation. The resulting z-score tells you how many standard deviations above or below the mean the observation lies, making it easy to compare values from different distributions. Dividing the observation by the mean would just scale by the average and ignores dispersion. Using the median instead of the mean shifts the center and isn’t the standard way to standardize. Taking the mean and dividing by the standard deviation doesn’t involve the actual observation, so it doesn’t reflect its position relative to the distribution.

Calculating a z-score standardizes an observation by showing how far it is from the average in units of spread. You subtract the mean from the observed value and then divide by the standard deviation. This centers the data at zero and scales it so that one unit equals one standard deviation. The resulting z-score tells you how many standard deviations above or below the mean the observation lies, making it easy to compare values from different distributions.

Dividing the observation by the mean would just scale by the average and ignores dispersion. Using the median instead of the mean shifts the center and isn’t the standard way to standardize. Taking the mean and dividing by the standard deviation doesn’t involve the actual observation, so it doesn’t reflect its position relative to the distribution.