Self-test 3.2 – Estimation of measurement uncertainty in chemical analysis

1. Which of the following equations are for calculation of the experimental standard deviation? (n – number of the measurements, x_i– measurand, x_m– arithmetic mean of the measurands)? There are two right answers.

2. A number of repeated measurements of the same measurand are performed and the mean value and standard deviation are calculated. Which of the following statements are true?

The mean can be calculated by summing up all results and dividing the sum with the number of obtained values.

In the case x is normally distributed with mean x_m and standard deviation s the probability of a next measurement result of x falling into x_m ± s is roughly 95%.

The mean can be calculated according to the equation X_m=(X₁+X₂+…+X_n) /n.

The standard deviation can be calculated according to equation X_m=(X₁+X₂+…+X_n) /n.

The mean can be calculated according to the equation X_m= X₁/n + X₂/n +…+X_n/n.

Standard deviation can be regarded as an estimate of measurement error.

The mean is always exactly in the middle of the largest and the smallest obtained value.

Standard deviation of a quantity x characterizes the spread of the values obtained from repeated measurements.

According to properties of the normal distribution the mean value is the most probable value for next result when doing a large number of repetitions.

Standard deviation expresses the difference of our measurement result from the true value.

The mean is always somewhere between the largest and the smallest obtained value.

3. Calculate the titration repeatability standard deviation when the titrant volumes consumed for titration of identical samples were (all in ml): 12.02; 11.96; 11.99; 12.00; 12.02.
Please present your answer with three decimals after comma.