- #1

theBEAST

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## Homework Statement

Here is a slide in my notes:

I am kind of confused about mean and standard deviation. So in my notes it says X1 to Xn are independent measurements. Then it says each independent measurement has a mean μ. But how is this possible, if they are independent measurements (in order words 1 measurement) how can you take the average of one measurement. Wouldn't it just mean the mean of one measurement is equal to the same value of the measurement? And is μ

_{X_bar}is the average of all the samples X1 to Xn? Is what I have said so far correct?

Moving on, it says there is some uncertainty for each independent measurement, this kind of makes sense to me. How I see it is if we make a length measurement with a ruler, the uncertainty on it may be +/- 0.5 mm assuming the smallest increments on the ruler is 1 mm. Thus, each independent measurement will have the same uncertainty. Is my interpretation correct? I feel kind of lost right now.