# Position of standard deviation

1. Jan 31, 2016

### jk22

Suppose i have a random variable X and its standard deviation dx. We could write the average with error like $$<X>\pm dx/2$$.

But how do we know it is centered or not ? It could be +1/4 -3/4 for example.

2. Jan 31, 2016

### Staff: Mentor

If you just know the standard deviation, you cannot know if the uncertainty is symmetric. If it is (significantly), which is an unlikely case, more information should be given, at least +x-y separately, but ideally the full likelihood distribution.

3. Jan 31, 2016

### jk22

Could we compute $$\int^{<X>}x^2P (X=x)dx$$ for the minus sign and above the average for the plus sign ?

4. Jan 31, 2016

### Staff: Mentor

5. Jan 31, 2016

### Staff: Mentor

The thing you should compute is called skewness:

https://en.m.wikipedia.org/wiki/Skewness#Definition

6. Jan 31, 2016

### Hornbein

You could look at the data and see whether it looks centered. Or you could know something about the situation that tells you whether to expect it to be centered or not.

Confidence intervals can be any shape you desire. You just have to have a good reason to choose such a shape.

Many people just assume everything is normally distributed. Sometimes it is, sometimes it isn't.
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