What is the relationship between variance and standard deviation?

What is the relationship between variance and standard deviation?

• A. Variance equals the square root of standard deviation
• B. They are independent
• C. Standard deviation equals the square root of variance
• D. Standard deviation is the square root of variance

Answer: (D)

Standard deviation is the square root of the variance. Variance measures how far data points deviate from the mean on average, but it sums the squared deviations, so its units are squared. Taking the square root converts that back to the original units, giving a spread measure you can interpret on the same scale as the data. So the standard deviation equals the square root of the variance. The idea that variance is the square root of standard deviation would mix up units and meaning, and the notion that they are independent ignores their direct mathematical connection.

Standard deviation is the square root of the variance. Variance measures how far data points deviate from the mean on average, but it sums the squared deviations, so its units are squared. Taking the square root converts that back to the original units, giving a spread measure you can interpret on the same scale as the data. So the standard deviation equals the square root of the variance. The idea that variance is the square root of standard deviation would mix up units and meaning, and the notion that they are independent ignores their direct mathematical connection.