You cannot just add the standard deviations. Instead, you add the variances. ... Standard deviation is defined as the square root of the variance . The other way around, variance is the square of SD.

How do you combine 2 standard deviations?

Namely, after we square the SDs, we divide each by its own sample size. Then add square root to get the combined standard deviation.

What happens to standard deviation when you add?

For standard deviation, it's all about how far each term is from the mean. ... In other words, if you add or subtract the same amount from every term in the set, the standard deviation doesn't change. If you multiply or divide every term in the set by the same number, the standard deviation will change.