Population and Sample

Study of statistics is the study of data. The two important types of data sets (and often confused) are Population and Sample.

• Population Data - Includes everything from the data set
• Sample Data - Well chosen sample from the Population

Throwing some more details:

Population Data

Examples:

• Semester grades of all students in Business Analytics class at UCSD
• Height of all current International Baseball players
• Daily usage of smartphones by all kids of age 6-13 in Canada

In practical, population data can be very huge. It is challenging to collect all the members of a Population. That is where sampling of data helps to draw conclusions.

Sample Data

• A subset of population
• A good sample represents the whole population

Differences

	Population	Sample
Measurable characteristic	Parameter	Statistic
Mean	μ ("mu")	x̅ ("x-bar")
Standard Deviation	σ ("sigma")	S
Variance	σ² ("sigma-squared")	S²

Formula Differences

Population Std. Deviation - $\sigma = {\sqrt{\sum (X - \mu)^2 \over n}}$

Sample Std. Deviation - $S = {\sqrt{\sum (x - \bar{x}^2) \over n-1}}$