Describing variability - standard deviation and coefficient of variation

3 Describing variability - standard deviation and coefficient of variation 

We have two tabletting machines producing erythromycin tablets with a nominal content of250 mg. The two machines are made by the Alpha and Bravo Tabletting Machine Corporations, respectively. Five hundred tablets are randomly selected 

The two machines are very similar in terms of average drug content for the tablets, both producing tablets with a mean very close to 250 mg. However, the two products clearly differ. With the Alpha machine, there is a considerable proportion of tablets with a content differing by more than 10 mg from the nominal dose (i.e. below 240 mg or above 260 mg), whereas with the Bravo machine, such outliers are much rarer. An indicator of dispersion is required in order to convey this difference in variability. 

Erythro content (mg) Deviation from mean Deviation squared Erythro content (mg) Deviation from mean Deviation squared 

The key step in the calculation is the production of the second column - the individual deviations from the mean. The first machine produces rather variable tablets and so several of the tablets deviate considerably (e.g. —13.7 or +15.3 mg) from the overall mean. These relatively large figures then feed through the rest of the calculation, producing a high final SD (8.72 mg). 

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DESCRIBING VARIABILITY - STANDARD DEVIATION AND COEFFICIENT OF VARIATION 17... 

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