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Wolfram MathWorld provides links to probability and statistics web resources.

The online textbook Statistics at Square One is a useful resource, particularly the chapter "Study design and choosing a statistical test".

There are two main types of statistics.

1. Descriptive statistics such as "The median number of friends on Facebook is 342" which describe a population

Image source: http://blog.stephenwolfram.com/2013/04/data-science-of-the-facebook-world/

2. Inferential statistics which seek to answer questions about set of data, such as "Does X Brand of anaesthetic cause less complications than Y Brand?"

In simple terms, this is done by mathematically comparing groups within the data (eg; XBrand or YBrand) and seeing if the Effect (statistical difference between groups of data) is larger than the Error (differences through random chance).

Business, Medicine, Psychology, and Math/Statistics students all use data and statistics in their studies.

In almost all cases data is only gathered from a sample population. How large and representative that sample is affects if statistics can be used to make statements or even predictions beyond the sample. Good statistics can significantly empower an argument or decision.

Statistics can be used to :

• Predict an outcome
• Test a hypothesis
• Compare information
• Provide information in a structured way

There are a number of different types of statistics:

• Incidence

         The number of specified new events
         e.g., persons falling ill with a specified disease 

• Mortality

         An estimate of the proportion of the population that dies during a specified period

• Survival

         The proportion of the population that is alive at a specific period in time despite the diagnosis of their disease/condition

• Prevalence

         The number of cases of a disease existing in a given population at a specific period of time (period prevalence)

(all definitions taken from Stedman's Medical Dictionary)