Examples of when to use the sample or population standard deviation
Q. A teacher sets an exam for their pupils. The teacher wants to summarize the results the pupils attained as a mean and standard deviation. Which standard deviation should be used?
A. Population standard deviation. Why? Because the teacher is only interested in this class of pupils' scores and nobody else.
Q. A researcher has recruited males aged 45 to 65 years old for an exercise training study to investigate risk markers for heart disease (e.g., cholesterol). Which standard deviation would most likely be used?
A. Sample standard deviation. Although not explicitly stated, a researcher investigating health related issues will not simply be concerned with just the participants of their study; they will want to show how their sample results can be generalised to the whole population (in this case, males aged 45 to 65 years old). Hence, the use of the sample standard deviation.
Q. One of the questions on a national consensus survey asks for respondents' age. Which standard deviation would be used to describe the variation in all ages received from the consensus?
A. Population standard deviation. A national consensus is used to find out information about the nation's citizens. By definition, it includes the whole population. Therefore, a population standard deviation would be used.
What are the formulas for the standard deviation?
The sample standard deviation formula is:
where,
s = sample standard deviation
= sum of...
= sample mean
n = number of scores in sample.
= population standard deviation
= population mean