Estimation of measurement uncertainty in chemical analysis

Self-test 3.4

Here you can test whether you have correctly understood the concept of standard deviation of the mean and its calculation.

1. A number of parallel measurements of a quantity X are performed on identical samples under identical conditions and values x₁, x₂, .. x_n are obtained. Mark the correct statements.

The standard deviation of the mean can be calculated according to equation

Standard deviation of the mean can be calculated by dividing the experimental standard deviation by the square root of the number of measurements.

Standard deviation of the mean can be calculated by dividing the experimental standard deviation by square root of three.

Standard deviation of the mean can be calculated by summing up all values and dividing the sum with the number of values.

Standard deviation of the mean is often denoted as s(x_m).

Standard deviation of the mean can be used as the estimate of standard uncertainty (caused by the repeatability) of X if the mean x_m is used as the value of X in the model.

2. Equation

is given. What are the symbols used in this equation?

1. s(x_m)	standard deviation of the mean Unselect i-th individual result Unselect arithmetic mean Unselect standard deviation Unselect number of measurements Unselect
2. s(x)	standard deviation of the mean Unselect i-th individual result Unselect arithmetic mean Unselect standard deviation Unselect number of measurements Unselect
3. x_m	standard deviation of the mean Unselect i-th individual result Unselect arithmetic mean Unselect standard deviation Unselect number of measurements Unselect
4. x_i	standard deviation of the mean Unselect i-th individual result Unselect arithmetic mean Unselect standard deviation Unselect number of measurements Unselect
5. n	standard deviation of the mean Unselect i-th individual result Unselect arithmetic mean Unselect standard deviation Unselect number of measurements Unselect