What does a z-score of 0 indicate?

What does a z-score of 0 indicate?

• A. The observation equals the mean.
• B. The observation is one standard deviation above the mean.
• C. The observation is at the median.
• D. The observation is twice the mean.

Answer: (A)

Z-scores tell you how far a value is from the mean in units of the standard deviation. A z-score of zero means the value is exactly at the mean, since z = (X − μ)/σ and setting z to 0 gives X = μ. For example, if the mean is 100 and the standard deviation is 15, a value of 100 has a z-score of 0. This point is the center of the distribution; a z-score of +1 would be one standard deviation above the mean, and a z-score of −1 would be one standard deviation below. The median can coincide with the mean in a symmetric distribution, but the zero z-score specifically indicates no deviation from the mean.

Z-scores tell you how far a value is from the mean in units of the standard deviation. A z-score of zero means the value is exactly at the mean, since z = (X − μ)/σ and setting z to 0 gives X = μ. For example, if the mean is 100 and the standard deviation is 15, a value of 100 has a z-score of 0. This point is the center of the distribution; a z-score of +1 would be one standard deviation above the mean, and a z-score of −1 would be one standard deviation below. The median can coincide with the mean in a symmetric distribution, but the zero z-score specifically indicates no deviation from the mean.