What is the Relative Standard Deviation?

Relative Standard Deviation Formula

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Standard Deviation σ = √ [Σ(x- μ)2 / N]

For example, in financial markets, this ratio helps quantify volatility. The RSD formula helps assess the risk involved in security regarding the movement in the market. If this ratio for security is high, then the prices will be scattered, and the price range will be wide. It means the volatility of the security is high. If the ratio for security is low, then the prices will be less scattered. It means the volatility of the security is low.

How to Calculate Relative Standard Deviation? (Step by Step)

Follow the below steps:

  • First, calculate the mean (μ), i.e., the average of the numbersOnce we have the mean, subtract the mean from each number, which gives us the deviation, and squares the deviations.Add the squared deviations and divide this value by the total number of values. It is the variance.The square root for the variance will give us the standard deviation (σ).Divide the standard deviation by the mean and multiply this by 100.Hurray! You have just cracked how to calculate the relative standard deviation formula.

To summarize, dividing the standard deviation by the mean and multiplying by 100 gives a relative standard deviation. That’s how simple it is!

Before we move ahead, there’s some information you should know. First, when the data is a population on its own, the above formula is perfect, but if the data is a sample from a population (say, bits and pieces from a bigger set), the calculation will change.

The change in the formula is as below:

Standard Deviation (Sample) σ = √ [Σ(x- μ)2 / N-1]

When the data is a population, it should be divided by N.

When the data is a sample, it should be divided by N-1.

Examples

Example #1

Marks obtained by 3 students in a test are as follows: 98, 64, and 72. But first, calculate the relative standard deviation.

Solution:

Below is given data for calculation

Mean

Calculation of Mean

μ = Σx/ n

where μ is the mean; Σxi is a summation of all the values, and n is the number of items

μ = (98+64+72) / 3

μ= 78

Standard Deviation

Therefore, the calculation of Standard Deviation  is as follows,

Adding the values of all (x- μ)2 we get 632

Therefore, Σ(x- μ)2 = 632

Calculation of Standard Deviation:

σ = √ [Σ(x- μ)2 / N]

=√632/3

σ = 14.51

RSD

Formula = (Standard Deviation / Mean) * 100

= (14.51/78)*100

Standard Deviation will be – 

RSD = 78 +/- 18.60%

Example #2

The following table shows prices for stock XYZ. Find the RSD for the 10 day period.

Below is given data for calculation of relative standard deviation.

μ = (53.73+ 54.08+ 54.14+ 53.88+ 53.87+ 53.85+ 54.16+ 54.5+ 54.4+ 54.3) / 10

μ = 54.091

σ = 0.244027

= (0.244027/54.091)*100

RSD = 0.451141

Formula Example #3

An organization conducted a health checkup for its employees and found that majority of the employees were overweight, the weights (in kgs) for 8 employees are given below, and you are required to calculate the Relative Standard Deviation.

μ = (130 + 120 + 140 + 90 + 100 + 160 + 150 + 110) / 8

μ = 125

σ = 24.4949

= (24.49490/125)*100

RSD = 19.6

Since the data is a sample from a population, the RSD formula needs to be used.

Relevance and Use

The relative standard deviation helps measure the dispersionDispersionIn statistics, dispersion (or spread) is a means of describing the extent of distribution of data around a central value or point. It aids in understanding data distribution.read more of a set of values related to the mean. It allows us to analyze the precision of a set of values. The value of RSD expresses in percentage. It helps to understand whether the standard deviation is small or huge compared to the mean for a set of values.

The denominator for calculating RSD is the absolute value of the mean, and it can never be negative. Hence, RSD is always positive. The standard deviation analyzes in the context of the mean with the help of RSD. RSD is used to analyze the volatility of securities. In addition, RSD enables the comparison of the deviation in quality controls for laboratory tests.

This article has been a guide to Relative Standard Deviation and its definition. Here, we learn how to calculate relative standard deviation using its formula, examples, and a downloadable Excel template. You can learn more about Excel modeling from the following articles: –

  • Standard Deviation Formula ExcelStandard Deviation Formula ExcelThe standard deviation shows the variability of the data values from the mean (average). In Excel, the STDEV and STDEV.S calculate sample standard deviation while STDEVP and STDEV.P calculate population standard deviation. STDEV is available in Excel 2007 and the previous versions. However, STDEV.P and STDEV.S are only available in Excel 2010 and subsequent versions.
  • read moreFormulaFormulaSample standard deviation refers to the statistical metric that is used to measure the extent by which a random variable diverges from the mean of the sample.read more of Sample Standard Deviation Of Sample Standard DeviationSample standard deviation refers to the statistical metric that is used to measure the extent by which a random variable diverges from the mean of the sample.read moreCalculate Portfolio Standard DeviationCalculate Portfolio Standard DeviationPortfolio standard deviation refers to the portfolio volatility calculated based on three essential factors: the standard deviation of each of the assets present in the total portfolio, the respective weight of that individual asset, and the correlation between each pair of assets of the portfolio.read moreCompare – Variance vs Standard DeviationCompare - Variance Vs Standard DeviationVariance is a numeric value that defines every observation’s variability from the arithmetic mean, while Standard Deviation is a measure to determine how spread out the observations are from the arithmetic mean. read moreSimple Random SamplingSimple Random SamplingSimple random sampling is a process in which each article or object in a population has an equal chance of being selected, and using this model reduces the possibility of bias towards specific objects.read more