What is relative standard deviation (RSD) and when is it used?

• A. RSD = (mean / standard deviation) × 100%
• B. RSD = (standard deviation / mean) × 100%; used to express precision relative to the mean.
• C. RSD is the difference between max and min
• D. RSD is log of the standard deviation

Answer: (B)

The concept being tested is how we quantify dispersion relative to the size of the measurements. Relative standard deviation, also known as the coefficient of variation, expresses how large the typical deviation is compared with the mean value. It is calculated as the standard deviation divided by the mean, multiplied by 100 to give a percentage.

This format is useful because it lets you compare precision across data sets that have different scales or units. For example, if one set has a larger average value than another, the same standard deviation would be more meaningful if viewed as a percentage of its mean; the RSD shows that proportionally how much the data vary. A smaller RSD means tighter clustering of data around the mean, indicating higher precision in measurements.

Be aware that RSD relies on a nonzero mean; if the mean is near zero, the RSD can become unstable or misleading. Also, the other options describe different things: a ratio of mean to standard deviation isn’t the standard way to express dispersion relative to the mean, the range is simply max minus min, and taking the log of the standard deviation isn’t a standard measure of dispersion.