Relative Standard Deviation Calculator

In mathematics, Relative Standard Deviation is nothing but the square root of variance and multiplied by 100 and divided by mean. To find the relative standard deviation of a sample, you must find the standard deviation. It is very easy to find the Relative Standard Deviation of a given sample, when we know the step by step process to find the standard deviation or variance.

By following the below points, you can easily solve the relative standard deviation of any sample.

• First, add all the numbers in the sample and square the total
• Divide the square of the total by number of data items in the sample
• Now, square each data item individually and add them all. Subtract the result number from the number obtained in step 2
• Divide the new number by (number of data items-1)
• Do the square root of that number to get the standard deviation
• Multiply standard deviation of sample by 100
• Find the sample mean
• Divide step 6 by the mean to get Relative Standard Deviation.

Example:

Question: What is the Relative Standard Deviation of sample {1, 2, 3, 4, 5,6}?

Solution

Given sample is {1, 2, 3, 4, 5,6}

Sum of data items in sample=1+2+3+4+5+6=21

(square of sum of numbers)/number of data items=21x21/6=73.5

Sum of squares of data items=1²+2²+3²+4²+5²+6²=1+4+9+16+25+36=91

91-73.5=17.5

Variance=17.5/(6-1)=17.5/5=3.5

Standard Deviation=sqrt(variance)=sqrt(3.5)

Relative Standard Deviation=SD*100/mean

Mean=Sum of data items/ number of data item

=21/6=3.5

RSD=sqrt(3.5)*100/3.5=53.45

Relative Standard Deviation is 53.4%

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

Relative standard deviation (RSD) is a special form of the standard deviation. It is obtained by multiplying standard deviation with 100 and dividing by mean.

2. How do you explain relative standard deviation?

Relative standard deviation is used to determine if the standard deviation of a set of data is large or small when compared to the mean. You can also tell that relative standard deviation is how you precise the average of results.

3. Is high relative standard deviation good or bad?

Standard deviations are neither good nor bad. They are indicators of how spread out your data is. The distributions having coefficient of variation more than 1 are considered as high where CV is less than 1 are considered to be low variance.

4. Which website provides the best tool to calculate Relative Standard Deviation?

Onlinecalculator.guru is a trusted website that offers a handy online calculator tool for finding the relative standard deviation of a sample. These free calculators make your calculations easier and faster..