How do you determine the uncertainty of a mean value?

To determine the uncertainty of a mean value, calculate the standard error of the mean.

The uncertainty of a mean value is a measure of the precision of the mean. It is calculated using the standard error of the mean (SEM), which is the standard deviation of the sample mean distribution. The SEM is calculated by dividing the standard deviation of the sample by the square root of the sample size.

For example, if a sample of 10 measurements has a standard deviation of 2, the SEM would be 2/√10 = 0.63. This means that the uncertainty of the mean value is ±0.63.

The uncertainty of the mean value can also be represented by a confidence interval. A 95% confidence interval means that there is a 95% chance that the true population mean falls within the range of the interval. The confidence interval is calculated by multiplying the SEM by the t-value for the desired level of confidence and adding/subtracting it from the mean value.

It is important to note that the uncertainty of the mean value can be reduced by increasing the sample size or by improving the precision of the measurements. Additionally, the uncertainty of the mean value should be reported alongside the mean value to provide a complete understanding of the data.