In statistics, a data set with all values the same has which property?

• A. Zero variance; constant data; mean equals all values
• B. High variance
• C. Skewed distribution
• D. Random sampling

Answer: (A)

When every value in a data set is the same, there is no variability in the data. This means the variance is zero because all observations deviate from the mean by zero. The data are constant, so the mean is equal to that common value. The standard deviation is also zero for the same reason. Other options don’t fit because a high level of spread would require differing values, a skewed distribution involves asymmetry in the data, and random sampling describes how data were collected rather than a property of the data values themselves.