Standard Deviation of zero means?

Standard Deviation of zero means?

• A. The mean equals zero.
• B. All scores are above the mean.
• C. There is no variability in the scores.
• D. The data are perfectly normally distributed.

Answer: (C)

Standard deviation measures how spread out the scores are around the mean. If it is zero, every score is exactly the same, so there is no variability at all. The mean could be any value; zero isn’t implied. This isn’t the same as a perfectly normal distribution, which requires some spread. When all data collapse to a single point, that’s a degenerate case, not a normal curve. So the statement that there is no variability in the scores best captures what a zero standard deviation means. The other statements don’t fit: the mean doesn’t have to be zero, all scores aren’t above the mean (they’re equal to it), and a degenerate point isn’t a normal distribution.

Standard deviation measures how spread out the scores are around the mean. If it is zero, every score is exactly the same, so there is no variability at all. The mean could be any value; zero isn’t implied. This isn’t the same as a perfectly normal distribution, which requires some spread. When all data collapse to a single point, that’s a degenerate case, not a normal curve. So the statement that there is no variability in the scores best captures what a zero standard deviation means. The other statements don’t fit: the mean doesn’t have to be zero, all scores aren’t above the mean (they’re equal to it), and a degenerate point isn’t a normal distribution.