## What is the Relative Standard Deviation?

Relative Standard Deviation (RSD) is the measure of deviation of a set of numbers disseminated around the mean and and is calculated as the ratio of standard deviation to the mean for a set of numbers. Higher the deviation, further the numbers are from the mean. Lower the deviation, closer the numbers are from the mean.

### Relative Standard Deviation Formula

**Relative Standard Deviation = (Standard Deviation / Mean) * 100**

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

To give an example, in financial markets, this ratio helps in quantifying volatility. RSD formula helps to assess the risk involved in security with regards to 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. This means the volatility of the security is high. If the ratio for security is low, then the prices will be less scattered. This means the volatility of the security is low.

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

**Step 1:**First, calculate the Mean (μ), i.e., the average of the numbers**Step 2:**Once we have the mean, subtract the Mean from each number, which gives us the deviation, squares the deviations.**Step 3:**Add up the squared deviations and divide this value with the total number of values. This is the variance.**Step 4:**Square root for the variance will give us the Standard Deviation (σ).**Step 5:**Divide the Standard Deviation by the Mean and multiply this by 100**Step 6:**Hurray! You have just cracked how to calculate the Relative Standard Deviation formula.

To summarize, by dividing the Standard Deviation by the mean and multiplying by 100 gives Relative Standard Deviation. That’s how simple it is!

Before we move ahead, there’s some information you should know. 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.

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### Examples

#### Example #1

**Marks obtained by 3 students in a test is as follows: 98, 64, and 72. 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.**

**Solution:**

Below is given data for calculation of relative standard deviation.

**Mean**

Calculation of Mean

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**

**Standard Deviation**

Therefore, the calculation of Standard Deviation is as follows,

Calculation of Standard Deviation:

σ =** 0.244027**

**RSD**

Formula = (Standard Deviation / Mean) * 100

= (0.244027/54.091)*100

**Standard Deviation will be – **

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.**

**Solution:**

Below is given data for calculation of relative standard deviation.

**Mean**

Calculation of Mean

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

μ = **125**

**Standard Deviation**

Therefore, the calculation of Standard Deviation is as follows,

Calculation of Standard Deviation:

σ = **24.4949**

**RSD**

Formula = (Standard Deviation / Mean) * 100

= (24.49490/125)*100

**Standard Deviation will be – **

RSD = **19.6**

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

### Relevance and Use

Relative Standard Deviation helps in measuring the dispersion of a set of values with relation to the mean, i.e.; it allows us to analyze the precision in a set of values. The value of RSD is expressed in percentage, and it helps to understand whether the Standard Deviation is small or huge when 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 is analyzed in the context of the mean with the help of RSD. RSD is used to analyze the volatility of securities. RSD enables to compare the deviation in quality controls for laboratory tests.

### Recommended Articles

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

- Standard Deviation Formula Excel
- Formula of Sample Standard Deviation
- Calculate Portfolio Standard Deviation
- Compare – Variance vs Standard Deviation
- Simple Random Sampling

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