Once you’ve determined your dataset’s standard deviation and mean, the RSD calculator (relative standard deviation calculator) can assist you in making judgments regarding it. Is the difference ‘great’ or ‘small’? How does your data stack up against other datasets? Continue reading to find out more.

Also, make sure to check our other related calculators, such as Relative Error Calculator, or this Mean Median Mode Calculator. Further, if you want to learn more about probability, see this Probability of 3 Events tool. Another statistical value is Population Density, so learn more about it, or maybe you want to learn something new about the Central Limit Theorem.

What is the relative standard deviation RSD?

So, the RSD stands for relative standard deviation and is a type of standard deviation and we express it as a percentage of the mean. The RSD is always in the positive direction.

The relative standard deviation is commonly written after the mean and with a plus-minus sign, such as 35 +-5%, where 5% represents the relative standard deviation.

Common uses for the RSD calculator

By comparing the standard deviation to the mean, relative standard deviation puts the standard deviation into context. Viewing standard deviation as RSD aids decision-making in a variety of scenarios, including:

  • A supermarket shop, for example, may mandate that the RSD of all fruit sizes be less than 10%.
  • We process the Stock price volatility.
  • To express the accuracy of an assay in analytical chemistry.
  • The variation of two separate datasets is being compared.

Relative standard deviation formula

\text{Relative standard deviation } = \frac{\text{ standard deviation }}{|mean|} * 100%</span>

When not to use relative standard deviation

The relative standard deviation calculator should not be used when 0 does not imply an absence of quantity, such as temperature in degrees Celsius or Fahrenheit.

So, if the average temperatures were 12 3°C one day and 1 3°C the next, the RSD would be 25% on the first day and 300% (a considerable increase!) on the second day.

Because 0°C is arbitrary, a mean temperature closer to it should not necessarily make departures from the mean appear larger. Instead, we determine a relative standard for temperatures stated in Kelvin.

Relative standard deviation and coefficient of variation

The method for calculating relative standard deviation is quite similar to the formula for calculating the coefficient of variation. The main difference is that the RSD calculator divides the standard deviation by the mean’s absolute value, whereas the coefficient of variation calculator divides it by the mean. As a result, the coefficient of variation might be positive or negative, although the relative standard deviation must always be positive.

The degree to which observations stray from an adequate measure of central tendency is referred to as dispersion, therefore we have two types of dispersion measures: absolute dispersion and relative dispersion. Further, variance and standard deviation are two forms of absolute measures of variability that reflect how the data is distributing around the mean. The average of the squares of the deviations is the variance.

On the other hand, the standard deviation is the square root of the numerical number produced when computing the variance. Many individuals make a distinction between these two mathematical ideas. As a result, the purpose of this essay is to clarify the fundamental distinction between variance and standard deviation.

Relative standard deviation – An example

John wants to stock his fruit stand with a new and exciting item. He can choose from a box of pears, apples, or pineapples. However, he wants to ensure that the fruits are consistent in weight for easy pricing. The mean and standard deviation of weight for each fruit is:

  • Pears: 100 ± 5 g.
  • Apples: 120 ± 34 g.
  • Pineapples: 2 ± 0.5 lbs.

Which fruit has the most consistent weight? For apples, the calculation would be:

(34 g / 120 g) * 100% = 28.3%

Try using the RSD calculator to convert the standard deviations into relative standard deviations.

Now we can see the mean and RSD of weight for each fruit:

  • Pears: 100 g ± 5%
  • Apples: 120 g ± 28.3%
  • Pineapples: 2 g ± 25%

John can now see that apples have the most consistent weight, with the standard deviation expressed as relative standard deviation.

Frequently Asked Questions

Is high relative standard deviation good or bad?

There is no such thing as an excellent standard deviation or a maximum standard deviation.

What is the relation between standard deviation and relative standard deviation?

Frequently, the relative standard deviation (RSD) is more convenient. It is calculated by multiplying the standard deviation by 100 and dividing the result by the average in percent.