Chemistry Calculations

Statistics & Quality Control

Mean/Average (unit)

The mean is the average of a series of numbers. Report to the same units and decimal places as the data.

$$\overline{x}=\frac{x_1+x_2+\mathrm{...}+x_n}{n}$$

Sample Standard Deviation

Use standard deviation when the mean of two methods is the same. Report as +1 decimal place more than the data.

$$s=\sqrt{\frac{\Sigma (x-\overline{x}{)}^2}{n-1}}$$where x = data and $\overline{x}=\text{Mean}$

Coefficient of Variation

$$CV=\frac{SD}{Mean}\ast 100$$

Westgard Rules

There are 4 reject rules and 2 warning rules:

• 1-3s (one control value exceeds the mean ±3 SD)
• 2-2s (two consecutive control values exceed the mean ±2 SD)
• R-4s (when one value exceeds the mean +2 SD and another value exceeds -2 SD within the same run so that the values are 4 SD different from each other)
• 4-1s (four consecutive control values exceed the mean ±1 SD)

Warning Rules:

• 1-2s (one control value exceeds the mean ±2 SD)
• R10x (ten consecutive values fall on one side of the mean)

Dilutions & Concentrations

Calculating Dilutions Using Dilution Factors and Total Volume

You can determine the amount of solute required for a dilution with a given dilution factor and final (total) volume.

$$DF=\frac{V_{total}}{V_{solute}}$$

$$V_{solute}=\frac{V_{total}}{DF}$$

DF = dilution factor (e.g., in a 1:250 dilution, the DF is 250)

You can then determine the amount of diluent/solvent needed from the calculated volume of solute required.

$V_{diluent}=V_{total}-V_{solute}$