So How Do I Quote My Uncertainty

2 When you have a lot of data Confidence interval knowing the population mean and standard deviation 

For a normal distribution with population mean /x and standard deviation a the symmetric interval about the mean containing a fraction 1 — a of the results is given by 

When we are dealing with means of n repeat measurements, the interval containing (1 — a) of the means is given by the standard deviation of the mean, an (see equation 2.4)  

Although the interval in equation 2.8 is often expressed as a probability interval for the population mean ( The true value lies in this interval with a probability of 95% ), it is not. The population mean /x is what it is with 100% probability. (The only problem is that we do not know it ) What the confidence interval tells us is that if a large number of repeats of our n experiments were performed under 

We can rearrange this equation to give a confidence interval on /x given x  

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