Statistics is a science dealing with the collection, analysis, interpretation, and presentation of numerical data.[1]

 

Statistics can be subdivided into two branches: descriptive statistics and inferential statistics.

Descriptive vs. Inferential Statistics

If a business analyst is using data gathered on a group to describe or reach conclusions about that group, the statistics is known as descriptive statistics. I.e. if one produces statistics on a subject and then uses those statistics to reach conclusions about that subject only, that is known as descriptive statistics.

 

Inferential Statistics is when a researcher gathers data from a sample and uses the statistics generated to reach conclusions about the population from which the sample was taken. I.e. the data gathered are used to infer something about a larger group.

 

Population is a collection of persons or objects with something in common.

Census is data gathered from the whole population for a given measurement of interest.

Sample is a portion of the whole and, with statistics, if a sample is properly taken it is representative of the whole. A sample is a subset of the population.

 

A parameter is a descriptive measure of the population. When you measure something in a population, it is called a parameter. Parameters are denoted by Greek letters. Examples include:

 

µ	population mean	mu
σ2	population variance	sigma square
σ	population standard deviation	sigma

 

A statistic is a descriptive measure of a sample. When you measure something in a population, it is called a statistic. Statistics are usually denoted by Roman letters. Examples of statistics are:

 

	sample mean	xbar
s2	sample variance
s	sample standard deviation

 

If I got the average age of parents in single-family homes, the measure would be called a parameter. If I measured the age of a sample of these same individuals it would be called a statistic. Thus, a population is to a parameter as a sample is to a statistic.[2]