Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Book summary
- 1813 keer gelezen
Join with a free account for more service, or become a member for full access to exclusives and extra support of WorldSupporter >>
Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 6 summary
SUMMARIZING POSSIBLE OUTCOMES AND THEIR PROBABILITIES
All possible outcomes and probabilities are summarized in a probability distribution. There is a normal and a binomial distribution. A random variable is a numerical measurement of the outcome of a random phenomenon. The probability distribution of a discrete random variable assigns a probability to each possible value. Numerical summaries of the population are called parameters and a population distribution is a type of probability distribution, one that applies for selecting a subject at random from a population.
The formula for the mean of a probability distribution for a discrete random variable is:
μ= ΣxP(x)
It is also called a weighted average, because some outcomes are likelier to occur than others, so a regular mean would be insufficient here. The mean of a probability distribution of random variable X is also called the expected value of X. The standard deviation of a probability distribution measures the variability from the mean. It describes how far values of the random variable fall, on the average, from the expected value of the distribution. A continuous variable is measured in a discrete manner, because of rounding. A probability distribution for a continuous random variable is used to approximate the probability distribution for the possible rounded values.
PROBABILITIES FOR BELL-SHAPED DISTRIBUTIONS
The z-score for a value x of a random variable is the number of standard deviations that x falls from the mean. It is calculated as:
The standard normal distribution is the normal distribution with mean 
and standard deviation 
. It is the distribution of normal z-scores.
PROBABILITIES WHEN EACH OBSERVATION HAS TWO POSSIBLE OUTCOMES
An observation is binary if it has one of two possible outcomes (e.g: accept or decline, yes or no). A random variable X that counts the number of observations of a particular type has a probability distribution called the binomial distribution. There are a few conditions for a binomial distribution:
- Two possible outcomes
Each trial has two possible outcomes. - Same probability of success
Each trial has the same probability of success - Trials are independent
The formula for the binomial probabilities for any n is:
The binomial distribution is valid if the sample size is less than 10% of the population. There are a couple of formulas for the binomial distribution:
and 
Access:
Public
This content is related to:
Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Book summary
Research Methods & Statistics – Interim exam 2 (UNIVERSITY OF AMSTERDAM)
Research Methods & Statistics – Interim exam 2 (UNIVERSITY OF AMSTERDAM)
- 1824 keer gelezen
Check more of this topic?
This content is used in:
Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Book summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 1 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 2 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 3 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 5 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 6 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 7 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 8 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 9 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 10 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 11 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 12 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 14 summary
- Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Chapter 15 summary
Search other summaries?
This content is also used in .....
Statistics, the art and science of learning from data by A. Agresti (fourth edition) – Book summary
This bundle contains a full summary for the book "Statistics, the art and science of learning from data by A. Agresti (third edition". It contains the following chapters:
1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15.
Work for WorldSupporter
JoHo can really use your help! Check out the various student jobs here that match your studies, improve your competencies, strengthen your CV and contribute to a more tolerant world
Check how to use summaries on WorldSupporter.org
Online access to all summaries, study notes en practice exams
- Check out: Register with JoHo WorldSupporter: starting page (EN)
- Check out: Aanmelden bij JoHo WorldSupporter - startpagina (NL)
How and why would you use WorldSupporter.org for your summaries and study assistance?
- For free use of many of the summaries and study aids provided or collected by your fellow students.
- For free use of many of the lecture and study group notes, exam questions and practice questions.
- For use of all exclusive summaries and study assistance for those who are member with JoHo WorldSupporter with online access
- For compiling your own materials and contributions with relevant study help
- For sharing and finding relevant and interesting summaries, documents, notes, blogs, tips, videos, discussions, activities, recipes, side jobs and more.
Using and finding summaries, study notes en practice exams on JoHo WorldSupporter
There are several ways to navigate the large amount of summaries, study notes en practice exams on JoHo WorldSupporter.
- Use the menu above every page to go to one of the main starting pages
- Starting pages: for some fields of study and some university curricula editors have created (start) magazines where customised selections of summaries are put together to smoothen navigation. When you have found a magazine of your likings, add that page to your favorites so you can easily go to that starting point directly from your profile during future visits. Below you will find some start magazines per field of study
- Use the topics and taxonomy terms
- The topics and taxonomy of the study and working fields gives you insight in the amount of summaries that are tagged by authors on specific subjects. This type of navigation can help find summaries that you could have missed when just using the search tools. Tags are organised per field of study and per study institution. Note: not all content is tagged thoroughly, so when this approach doesn't give the results you were looking for, please check the search tool as back up
- Check or follow your (study) organizations:
- by checking or using your study organizations you are likely to discover all relevant study materials.
- this option is only available trough partner organizations
- Check or follow authors or other WorldSupporters
- by following individual users, authors you are likely to discover more relevant study materials.
- Use the Search tools
- 'Quick & Easy'- not very elegant but the fastest way to find a specific summary of a book or study assistance with a specific course or subject.
- The search tool is also available at the bottom of most pages
Do you want to share your summaries with JoHo WorldSupporter and its visitors?
- Check out: Why and how to add a WorldSupporter contributions
- JoHo members: JoHo WorldSupporter members can share content directly and have access to all content: Join JoHo and become a JoHo member
- Non-members: When you are not a member you do not have full access, but if you want to share your own content with others you can fill out the contact form
Quicklinks to fields of study for summaries and study assistance
Field of study
- All studies for summaries, study assistance and working fields
- Communication & Media sciences
- Corporate & Organizational Sciences
- Cultural Studies & Humanities
- Economy & Economical sciences
- Education & Pedagogic Sciences
- Health & Medical Sciences
- IT & Exact sciences
- Law & Justice
- Nature & Environmental Sciences
- Psychology & Behavioral Sciences
- Public Administration & Social Sciences
- Science & Research
- Technical Sciences
Check the related and most recent topics and summaries:
Activity abroad, study field of working area:
Institutions, jobs and organizations:
Add new contribution