What is the relationship between standard deviation and variance?

What is the relationship between standard deviation and variance?

• A. The standard deviation is the square of the variance
• B. The standard deviation is the square root of the variance
• C. They are unrelated
• D. The standard deviation is twice the variance

Answer: (B)

The standard deviation is the square root of the variance. Variance measures how spread out data are by averaging the squared deviations from the mean, which keeps all deviations positive and emphasizes larger ones. Taking the square root brings that measure back to the same units as the original data, making it easier to interpret. So if the variance is 4, the standard deviation is 2. The variance is in squared units, while the standard deviation matches the data’s units. That’s why the other ideas don’t fit: the standard deviation isn’t the square of the variance (that would give 16 in the example), it’s not unrelated, and it isn’t simply twice the variance (that would give 8 in the example).

The standard deviation is the square root of the variance. Variance measures how spread out data are by averaging the squared deviations from the mean, which keeps all deviations positive and emphasizes larger ones. Taking the square root brings that measure back to the same units as the original data, making it easier to interpret. So if the variance is 4, the standard deviation is 2. The variance is in squared units, while the standard deviation matches the data’s units.

That’s why the other ideas don’t fit: the standard deviation isn’t the square of the variance (that would give 16 in the example), it’s not unrelated, and it isn’t simply twice the variance (that would give 8 in the example).