The terms population and sample are found in just about all of the topics in statistics. A population is the entire group of interest, and the sample is a collection of some of the objects from the population. 

The standard deviation is a measure of the spread of the data about the mean. The more the data deviate from the mean, the higher the value of the standard deviation. 

For example, suppose five students all scored a 15 on a 20-point quiz: 15 15 15 15 15. The mean is 15 and because the data do not deviate from the mean of 15, the value of the standard deviation is 0.

For example, suppose you have the population data 5 10 15 20 25; the mean is 15. Notice the values deviate from the mean of 15. In this case, the population standard deviation is calculated to be 7.07.

For example, suppose you have the population data 5 5 5 15 25 25 25; the mean is 15. Notice that the data deviate more from the mean of 15 than the data did in the previous example, so the standard deviation of the population will be higher. It is calculated to be 9.26. 

Notes: 

• Population standard deviation, σ (lower case Sigma).

• Sample standard deviation, s. 

• Be careful when taking a quiz or test as to which set of data is involved: population or sample.  The standard deviation formulas differ slightly.

ALEKS Calculator Buttons

The ALEKS Calculator only has the button for sample standard deviation, it does NOT have a button for the population standard deviation.

To find the population standard deviation:

You are welcome to use an outside resource.

Calculator website:  Standard deviation calculator