Standard Deviation

Sigma dispersion standard deviation symbol

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:

  1. You have the entire population.
  2. 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):

  1. 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)

  1. Calculate the mean of the data set (x-bar)
  2. Subtract the mean from each value in the data set
  3. Square the differences found in step 2.
  4. Add up the squared differences found in step 3.
  5. Divide the total from step 4 by (n – 1) for sample data
  6. (Note: At this point you have the variance of the data).
  7. 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)

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

standard deviation example

 

Standard Deviation and Variance

Variance is Std Dev ^2.

Std Dev = Sqrt(variance)

Standard Deviation Videos

Video on Variance

The Normal Curve and Standard Deviation

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