Standard deviation is used to measure the amount of variation in a process. Standard Deviation is one of the most common measures of variability in a data set or population.

There are 2 types of equations: Sample and Population.

## What is the difference between Population and Sample.

Population refers to ALL of a set and sample is a subset. We most often have a sample and are trying to infer something about the whole group. However, if we want to know a truth of a subset of a whole population, use the Population equation.

### Use Population When:

- You have the entire population.
- You have a sample of a larger population, but you are only interested in this sample and do not wish to generalize your findings to the population.

### Use Sample When (Most often):

- If all you have is a sample, but you wish to make a statement about the population standard deviation from which the sample is drawn, you need to use the sample standard deviation.

**Remember:** It is impossible to have a negative standard deviation.

## How to Measure the Standard Deviation for a Sample (s)

Standard Deviation for a Sample (s)

- Calculate the mean of the data set (x-bar)
- Subtract the mean from each value in the data set
- Square the differences found in step 2.
- Add up the squared differences found in step 3.
- Divide the total from step 4 by (n – 1) for sample data
- (Note: At this point you have the variance of the data).
- Take the square root of the result from step 5 to get the standard deviation

### Example of Standard Deviation for a Sample (s)

- Chips per cookies in a batch
- Depth of river

Example of Standard Deviation for a Sample (s)

## How to Measure the Standard Deviation for a Population (σ)

Standard Deviation for a Population (σ)

- Calculate the mean of the data set (μ)
- Subtract the mean from each value in the data set
- Square the differences found in step 2.
- Add up the squared differences found in step 3.
- Divide the total from step 4 by N (for population data).
- (Note: At this point you have the variance of the data).

- Take the square root of the result from step 5 to get the standard deviation

### Example of Standard Deviation for a Population (σ)

Example of Standard Deviation for a Population (σ)

## Example Question: What is the standard deviation?

Nana’s Bakery wants to optimize the consistency of their cakes. The recipe calls for a certain number of eggs. The problem is that there is variation in egg sizes. Six eggs were randomly selected and the following weights were recorded (measured in ounces).

2.25; 1.75; 2.0; 2.5; 1.8

What is the standard deviation of the egg weights?

## Standard Deviation and Variance

Variance is Std Dev ^2.

Std Dev = Sqrt(variance)

## Comments (14)

Thanks a lot!

Very welcome, Roberto.

I really appreciate your explanations.

You’re welcome, Sonia. Happy to help!

How is this related to Six Sigma where we are expected to see a 99.9996 ?

Sashi, the sigma in Six Sigma refers to standard deviation. Six Sigma refers to what percentage is under the curve at six sigmas – or standard deviations from center. Does that help?

I am understanding now. thanks

Glad to hear it, Sharon!

Please advise vsf targets and minimum vs maximum Range and if no maximum Range do we have ranking for ex..

1 to 2 is controlled

3 to 4 is out of control

4 to 5 is above cout of control

When d2 changes the cp and cpk values are varrying. If so what will be the spec for each subgroup size.

i have a question

Let’s assume that based on a customer survey, the weight of a product is approved at the best acceptable level of 120 grams +- 12 grams . standard deviation of each product labled .If the standard deviation of a product is 6, what is the level of the sigma? If it is the 10 what the sigma level

So you want to determine the Sigma level of a process given a Standard Deviation? What have you tried?

Estimation of standard deviation depends on what

Specification limits

Target/Nominal value

Observed data

None of the above

This is a neat question, Arun.

To answer I recommend looking at each of the options you listed and asking what each has to do with Standard Deviation, if anything.

What are your thoughts?