Relative standard deviation is a common formula used in statistics and probability theory to determine a standardised measure of the ratio of the standard deviation to the mean. This formula is useful in various situations, including when comparing your own data to other related data and in financial settings, such as the stock market. Knowing how to calculate relative standard deviation may help you easily analyse and prepare numerical data. In this article, we discuss the definition of relative standard deviation when this formula is most appropriately used and the steps you can use to calculate the relative standard deviation.
Relative standard deviation, or RSD or the coefficient of variation, determines if the standard deviation of a set of data is small or large when compared to the mean. In other words, the relative standard deviation can tell you how precise the average of your results is. This formula is most frequently used in chemistry, statistics and other math-related settings, but is also the process to assess finances and the stock market.
The higher the relative standard deviation, the more spread out the results are from the mean of the data. On the other hand, a lower relative standard deviation means that the measurement of data is more precise.
To calculate the relative standard deviation, the formula is:
(S x 100)/x = relative standard deviation
In this formula, S represents the standard deviation and x represents the mean of the data being used. Following are the steps you can use to calculate this formula to determine the relative standard deviation:
- Calculate the mean
Compute the mean of the numbers in the data of your equation. The mean is simply the average of the numbers in your data set. You can calculate it by finding the sum of all the numbers and dividing it by the number of values in your data. For instance, if you have the following values X, Y and Z, the formula for the mean is (X + Y + Z) / 3. - Subtract the mean
Subtract the value of the mean from each number in the data to discover the deviation for each number. The deviation is the amount by which a numerical value differs from a fixed value like the mean. Hence, if (X + Y + Z) / 3 = M, the deviation for each number is X – M, Y – M and Z – M. - Square the values
Square the deviations for each of the numbers. In simple terms, it means multiplying each value by itself. Using the illustration above, you can compute it as (X – M) x (X – M), (Y – M) x (Y – M) and (Z -M) x (Z – M). - Find the sum of the squared values
In this stage, you’re to add together the squared deviations. These are the individual answers got from the multiplication of each deviation by itself. Hence, if (X – M) x (X – M) = XA, (Y – M) x (Y – M) = YB and (Z -M) x (Z – M) = ZC, their sum is XA + YB + ZC. - Divide it by the number of values
Here, you divide the sum of the squared deviations by the total number of values used to get the variance. From the illustration above, the number of values in the data set is 3. Hence, if XA + YB + ZC = XYZD, divide it by 3 to get XYZD / 3. - Calculate the standard deviation
You can find the square root of the variance to get the standard deviation of the data. We can depict this as √ (XYZD / 3), following the illustration above. Ensure you pay attention to the tiny details of the answer you get, especially if it has decimals. - Multiply it by 100
Multiply the standard deviation you have by 100. Next, divide your answer by the value of the mean. Your result is the relative standard deviation.
some situations that may require you to use this formula:
It’s useful for performing an industry or competitor analysis. You can a relative standard deviation when you want to compare your data with a colleague in your field or a similar company’s data.
This formula is useful for evaluating economic trends. When gauging the level of economic equality or inequality in society, a relative standard deviation can help you determine how certain variables related to the finances of the residents.
You may require it for computing equations. For instance, when you’re performing a statistics equation, some of them may require the relative standard deviation of a dataset to get the mathematical results you seek.
It’s essential in the production process of chemicals or other substances. When you’re trying to discover the level of homogeneity of a mixture in an industrial solids processing setting, your job may require you to calculate the relative standard equation.
It’s vital for performing customer analysis. You can use it when you’re trying to understand the product demands, trends and expected preferences of the consumers within an industry.
You can use it in stock market evaluation. When you’re analysing the possibility of a stock price advancing with the growth of the company for your employer, it may require you to first determine the relative standard deviation of the set of values you have gained.
You may require it to perform a risk assessment. To discover the risk-to-return ratio across multiple investment proposals, you can calculate the relative standard deviation of the data.
It’s beneficial for conducting sales analysis. When you’re computing the expected demand of production based on historical data to help you determine if you can recommend a reduction in product prices to boost sales in the company, it’s advisable to calculate a relative standard deviation.
Relative Standard Deviation Formula
Relative standard deviation is also called percentage relative standard deviation formula, is the deviation measurement that tells us how the different numbers in a particular data set are scattered around the mean. This formula shows the spread of data in percentage.
If the product comes to a higher relative standard deviation, that means the numbers are very widely spread from its mean.
If the product comes lower, then the numbers are closer than its average. It is also knows as the coefficient of variation.
The formula for the same is given as:
Where,
RSD = Relative standard deviation
s = Standard deviation
= Mean of the data.
Solved Examples
Question 1: Following are the marks obtained in by 4 students in mathematics examination: 60, 98, 65, 85. Calculate the relative standard deviation ?
Solution:
Formula of the mean is given by:
=
=
Calculation of standard deviation:
60 -17 289
98 21 441
65 -12 144
85 8 64
Formula for standard deviation:
S =
S =
S = 17.66
Relative standard deviation =
=
= 22.93%.
