If we have made the following several measurements of the quantity x that follow a normal distribution:
86, 85, 84, 89, 85, 89, 87, 85, 82, 85
The mean is 85.7 and the standard deviation(std) is about 2.
My textbook says that if we take a second measurement, then its uncertainty is the standard deviation. Could someone explain to me the logic behind this. I know there is a 68% confidence for the measurement to be 1 std away from the correct value so if my measured value is actually 2 stds away from the correct value then using the value of 1 std as an uncertainty doesn't even give range that includes the correct value in fact it is way far from the correct value. So could someone explain why we use the standard deviation as the uncertainty of individual measurements?