Which statement correctly links variance to the distribution of data around the mean?

Which statement correctly links variance to the distribution of data around the mean?

• A. It defines the central value of the data.
• B. It defines the distribution of data around the mean.
• C. It measures the sampling error.
• D. It is the same as the population parameter.

Answer: (B)

Variance measures how spread out data are around the mean. It does this by averaging the squared deviations of each value from the mean, so a larger variance means data are more dispersed and the distribution is wider around the central value. This directly ties variance to the idea of dispersion about the mean, rather than defining the mean itself or describing sampling error. While variance can be a population parameter (sigma^2) or a sample statistic (s^2), saying it is simply the same as the population parameter isn’t precise; the key point is that variance quantifies spread around the mean.

Variance measures how spread out data are around the mean. It does this by averaging the squared deviations of each value from the mean, so a larger variance means data are more dispersed and the distribution is wider around the central value. This directly ties variance to the idea of dispersion about the mean, rather than defining the mean itself or describing sampling error. While variance can be a population parameter (sigma^2) or a sample statistic (s^2), saying it is simply the same as the population parameter isn’t precise; the key point is that variance quantifies spread around the mean.