# What is the difference between standard deviation and variance?

I have been learning discrete probability and know that variance and sd are both measures of spread. I also know that sd is just the variance squared. But I don't know the difference between them. Do they measure different types of spread?

Also, I know that the expected value is used in terms of a full census so the mean is called the expected value. In a sample, however, the mean is just called the mean and is only an approximation of $$\mu$$ (E(x)). Similarly, $$S$$ is an approximation of $$\sigma$$. But is there such thing as an approximation of $$Var(x)$$ in a sample?

• What's the difference between a number $x$ and the number $\sqrt{x}$? They contain essentially the same information. Oct 16, 2020 at 10:36
• ahh ok. That's a nice insight. So why bother with sd and the square if x contains the same information for both? Oct 16, 2020 at 11:15
• Good point, after all we don't go squaring the mean Oct 16, 2020 at 11:24
• Yes, exactly. Any other discussions online are very vague about the answer to this question and I'm yet to find a suitable explanation Oct 16, 2020 at 11:40