Which of the following is true about $\mathrm{variance}$?

• A. $\mathrm{Variance}$ is the square of the $\mathrm{standard\; deviation}$.
• B. $\mathrm{Variance}$ is calculated by taking the square root of the mean of squared deviations.
• C. $\mathrm{Variance}$ is always measured in the same units as the original data.
• D. $\mathrm{Variance}$ can never be zero.

Answer: (A)

Verified step by step guidance

1. Recall the definition of variance: Variance measures the average squared deviation of each data point from the mean of the data set.
2. Understand the relationship between variance and standard deviation: The standard deviation is the square root of the variance, so variance is the square of the standard deviation.
3. Analyze the units of variance: Since variance involves squaring deviations, its units are the square of the original data units, not the same units as the data.
4. Consider the possibility of variance being zero: Variance can be zero if all data points are identical, meaning there is no deviation from the mean.
5. Evaluate each statement based on these concepts to determine which one is true.