If a dataset has a standard deviation of 0, what does that signify?

• A. The data points are widely spread
• B. There is no variability
• C. The mean is very high
• D. The data is normally distributed

Answer: (B)

A standard deviation of 0 indicates that all the data points in the dataset are identical. When the standard deviation is zero, it means that there is no variability among the data points; they all have the same value. This uniformity means that every individual data point is equal to the mean, leading to no dispersion or spread within the dataset.

In the context of statistical analysis, this concept underscores the importance of variability. While a dataset with variation (i.e., a standard deviation greater than zero) can provide insights into the distribution and spread of data points, a standard deviation of zero suggests a complete lack of diversity in the data being analyzed.