# Standard Deviation vs. Relative Standard Deviation

Standard deviation is the amount of deviation from the mean value of a given set of data. whereas relative standard deviation is a type of standard deviation. Standard deviation measures how precise your results are. It shows the closeness of the results to the mean value.

Whereas relative standard deviation measures the standard deviation or precision of the mean value. Standard deviation is abbreviated as SD whereas relative standard deviation is abbreviated as RSD.

The terms standard deviation and relative standard deviation are most frequently used in chemistry, math, and statistical calculations. These terms are used to measure the precision of results. Standard deviation measures the closeness of result to mean value whereas relative standard measures degree of standard deviation. It tells whether the standard deviation is small or large. RSD and SD predict the performance of an analysis. If these values are small then our analysis is more precise and vice versa.

## Standard deviation (SD)

The term standard deviation was used in writing by Karl Pearson in 1894. This was a replacement for earlier alternative names for the same idea: for example, “mean error” (Gauss), “mean square error,” and “error of mean square. Standard deviation is the comparison of individual results to the mean of that results.

Standard deviation is a measure of dispersion. It is calculated as the square root of the variance. It shows the closeness of the result to the mean value. Lower standard deviation shows results are more closer to the mean value. Lower the standard deviation greater would be precision in result.

Standard deviation can not be negative. Standard deviation measure the random errors. It measures the variation in a provided set of data. Standard deviation measures the distance between each data point and mean point. Its calculation depends upon whether we are finding population standard deviation or sample standard deviation.

### Types of Standard deviation

There are two main types of standard deviation

1. Population standard deviation
2. Sample standard deviations

#### Population standard deviation

Population standard deviation is the parameter that is calculated from every member of the population. Population standard deviation is used for large data calculations. i.e entire city etc. It is represented by the Greek letter sigma ‘σ’. Population standard deviation is always less than sample standard deviation.

How to calculate population standard deviation

Population standard deviation is calculated by dividing by the total number of individuals.

Formula

• σ = population standard deviation
• ∑ = sum of…
• x = each value
• μ = population mean
• N = number of values in the population

#### Sample standard deviation

Sample standard deviation is statistical data that is randomly selected from a few of individuals in a population. Sample standard deviation is used for the small data. It is represented by the Latin letter ‘s’. Sample standard deviation is always higher than population standard deviation.

How to calculate sample standard deviation

sample standard deviation is calculated by dividing by one less than the total number of individuals.

Formula:

• s = sample standard deviation
• ∑ = sum of…
• x = each value
• x̅ = sample mean
• n = number of values in the sample

### How to calculate standard deviation

Steps to find standard deviation are

Step 1

Find the mean value of provided data (μ).

Step 2

Find the deviation of values from the mean

Step 3

Take the square of each deviation

Step 4

Add all of the squared deviations (∑).

Step 5

Find the variance of provided date by dividing with N in case of population or n-1 in case of sample standard deviation.

Step 6

Take the square root of the variance

For example

Given data:

12, 15, 13, 13, 19, 18

Steps for calculation of the standard deviation
x x-x̅(x-x̅)2
1215-39
1415-11
1315-24
1415-11
1915416
181539
Variance = = (for population standard deviation)

Variance= (for Sample standard deviation)

(Population)
(Sample)

## Relative Standard deviation (RSD)

Relative standard deviation is related to standard deviation. It tells us whether the value of standard deviation is large or small when compared with the mean value. It tells us how close our results are to mean value. The smaller the RSD greater would be precision in results and vice versa. RSD is more convenient. It is expressed in percentage. It is most widely used for the interpretation of business, math, statistical, or analytical data. RSD is also known as the coefficient of variation.

### How to find the Relative standard deviation

Relative standard deviation is calculated from the standard deviation. It is also expressed in percentage. It is calculated by dividing the obtained standard deviation by mean value and then multiplying with 100.

### Formula of Relative standard deviation

(for sample standard deviation)

(for population standard deviation)

Percentage relative standard deviation

• s = standard deviation
• = mean value

Calculations:

From above mention example

s = 2.82

= 15

Putting values in formula

RSD =

And

%RSD =

### Relative standard deviations in HPLC

HPLC is commonly used in different types of analysis. Especially in pharmaceutical industries, it is used on daily basis for analysis of different types of drugs. Precision in our results depends upon the value of RSD. When RSD is a smaller value then our results are more precise. RSD is one of the important parameters of system suitability.

Different pharmacopeias provide RSD limits depending upon the number of injections. If results lie within the provided limit then it is suitable for that type of analysis otherwise it is not. The most commonly used concept in the pharmaceutical analysis is RSD will not be more than 2%. But it is not the same in all cases.

### USP limits of RSD

Number of individual injections
3456
Upper LImitMaximum permitted RSD
2.0%0.41%0.59%0.73%0.85%
2.5%0.52%0.74%0.92%1.06%
3.0%0.62%0.89%1.10%1.27%

## Excel sheet For calculations

Excel sheet mn ny bnae hoe ha jis mn RSD SD %RSD mean sb aik mn he ha but wo add nai ho rahe ????????///

Aur es mn ik sy 2 graph b dalny hn

## Concept bergs

What is the standard deviation?

Standard deviation is the amount of deviation from the mean value of a given set of data. Standard deviation is measure of dispersion. Standard deviation measures how precise your results are. It shows the closeness of the results to the mean value. Standard deviation is abbreviated as SD.

Differentiate between population and sample standard deviation.

Population Standard deviation Sample standard Deviation
It is used for large data analysis.It is used for small data analysis.
It is calculated from every member of a population.Data is randomly selected from a few individuals of the population.
It is represented by the Greek letter It is represented by Latin letter ‘s’
It is smaller than the sample standard deviation.It is higher than the population standard deviation.
It is calculated by dividing by the total number of individuals.It is calculated by dividing variance by one less than a total number of individuals.

Define relative standard deviation.

Relative standard deviation is the special type of standard deviation that tells us whether a standard deviation is small or large. Relative standard deviation is also known as the coefficient of variation.

How do I calculate the standard deviation?

Steps for calculation of the standard deviation

Step 1

Find the mean value of provided data (μ).

Step 2

Find the deviation of values from the mean

Step 3

Take the square of each deviation

Step 4

Add all of the squared deviations (∑).

Step 5

Find the variance of provided date by dividing with N in case of population or n-1 in case of sample standard deviation.

Step 6

Take the square root of the variance

What does standard deviation tell us?

Standard deviation tells us how much our data is deviating from the mean value. It also tells us how precise our results are. It provides information about the distribution of data.

Which is the better high or low standard deviation?

In analytical calculation lower the standard deviation greater would be precision. So low standard deviation is better than a high standard deviation.

Differentiate between mean and standard deviation.

Standard deviation is the distribution of data or deviation of individuals results from mean value whereas mean is average of given data.

What is the relative standard deviation in analytical chemistry?

In analytical chemistry relative standard deviation is related to precision. It is about how accurately we are performing analysis.

Does RSD mean accuracy or precision?

RSD is a comparison of results with the mean value. So it is related to precision.

How do we interpret from Standard deviation?

Standard deviation tells us how much we are away from the mean value. How our data is spreading out. In analytical chemistry, it tells us about precision in our results.

What are the limits of RSD in HPLC analysis?

According to USP

Number of individual injections
3456
Upper LImitMaximum permitted RSD
2.0%0.41%0.59%0.73%0.85%
2.5%0.52%0.74%0.92%1.06%
3.0%0.62%0.89%1.10%1.27%

Which is better RSD or SD?

RSD is better than SD. because it tells us about standard deviation.

What is the acceptable value for standard deviation?

There is no standard acceptable value for standard deviation. It acceptable value varies with type of analysis. Most commonly used value is NMT

What Does Variance Mean?

Variance is the square of standard deviation. It measure of variability of given data.

Formula =

Variance = 𝛔 2 or s2

What Are the Shortcomings of Variance?

Aur ya saeed bai sy likhvaon ga

How Do You Find the Standard Deviation Quickly?

Eska answer b steps wala ha

## Reference books

Probability, Statistic and Estimation by Mathieu ROUAUD

USP limits of RSD

## References:

A step by Step guide

Standard deviation by Wikipedia.