Back To Course

Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Kevin Newton*

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

Want proof that all of this normal distribution talk actually makes sense? Then you've come to the right place. In this lesson, we look at sampling distributions and the idea of the Central Limit Theorem, a basic component of statistics.

Statisticians sound pretty sure of themselves when talking about normal distribution. But, what makes them so confident that it works? After all, couldn't there be other **sample distributions**, the name given to the graphical result of incidences? Look, I understand your skepticism. I'll tell you what, take two dice, roll them, and add the results. If you were a betting woman, I'd say if you did that 10 times, you would get more 5s, 6s, and 7s than anything else. Go ahead, you can press the pause button. I'll be here.

Did it work out like I said? Or was I wrong? If I was wrong, go ahead and do the same thing again another 90 times. Trust me, I'll be waiting.

Countless statistics students have expressed the same doubt that some of you may have. Countless other statisticians have used supercomputers to run millions and billions of those operations. What they have come up with is the **normal distribution**, a roughly bell-shaped distribution that occurs over and over throughout populations and samples. Simply put, when something is staring you back in the face as obvious, statisticians tend not to ignore it, especially when it's as useful as the normal distribution.

On many graphs of normal distributions, you'll see that there's a line that runs right through the middle, at the highest point of the curve. This is aptly named the central line, and has a theorem named after it. The **central limit theorem** states that if you run a random experiment enough times the results will follow a normal distribution. In fact, the central limit theorem also states that the greater the opportunity for deviation amongst the variables, the greater that the final curve will resemble a normal distribution. Adding the results of two dice together will definitely look like a normal distribution given enough rolls, while adding four or five dice together on each throw will look like a normal distribution much earlier.

Of course, such a regular prediction of data is only useful as long as we can protect it from corruption. Everything must be random. If you were using a set of loaded dice, then chances are your graph looks quite different than mine. The same goes if you were not making sure that each roll of the rice was an honest attempt at randomness.

Across a larger population, we can't always double check every input to make sure that it was free of influence from any other data. However, we can still make special note of cases that exist that would corrupt such data.

Let's say that you had a class of students that was normally distributed in height and randomly selected from the student body at large. If you were going to expand that class from 30 to 40, the data set only maintains integrity if the new students are drawn from a random sampling of students. If, on the other hand, your class is suddenly flooded with members of the basketball team who chose to take the class in particular, the result could change. As basketball players are statistically taller than the rest of the population, your class would no longer have a normal sample.

Why do we care that the data sets inevitably end up on a normal distribution? In short, because it means that we can understand it much more implicitly. If a data set were not normally distributed, we would have to resort to calculus to figure out much of anything about the nature of the data, including finding new equations for every set of numbers. With a normal distribution, we simply have to find the **Z-score**, a measure of distance from the mean in terms of numbers of standard deviation, and then check a pre-made table to find the relevant percentages.

In this lesson we examine the concepts of a sampling distribution and the central limit theorem. A **sampling distribution** is the way that a set of data looks when plotted on a chart. As data sets grow, these have a tendency to mirror normal distributions. The **normal distribution** is a roughly bell-shaped distribution that occurs over and over throughout populations and samples. This is especially true as the sets have greater opportunity to span out over possible values. The reason for this is the **central limit theorem**, which states that the more an experiment is run, the more its data will resemble a normal distribution. However, this only holds if each new point is random in nature, as our example of flooding a normally distributed class with basketball players demonstrated. With a normal distribution, we can avoid calculus and find the **Z-score**, a measure of distance from the mean in terms of numbers of standard deviation, and then check a pre-made table to find the relevant percentages.

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
7 in chapter 7 of the course:

Back To Course

Statistics 101: Principles of Statistics11 chapters | 141 lessons | 9 flashcard sets

- Go to Probability

- Simple Random Samples: Definition & Examples 5:10
- What is Random Sampling? - Definition, Conditions & Measures 5:55
- Stratified Random Samples: Definition, Characteristics & Examples 6:25
- Cluster Random Samples: Definition, Selection & Examples 6:44
- Systematic Random Samples: Definition, Formula & Advantages 8:37
- Understanding the Law of Large Numbers 5:14
- Sampling Distributions & the Central Limit Theorem: Definition, Formula & Examples 5:06
- Finding Probabilities About Means Using the Central Limit Theorem 4:24
- Go to Sampling

- Effective Delegation Skills for Supervisors
- ORELA Essential Academic Skills: Practice & Study Guide
- Math 108: Discrete Mathematics
- ORELA Elementary Education - Subtest II: Practice & Study Guide
- ORELA Special Education: Practice & Study Guide
- Relations Between Labor & Management
- Managing Delegation
- Task Delegation
- Introduction to Delegation
- Delegation Within Teams
- How to Request a CLEP Transcript
- CLEP Exam Dates & Testing Center Locations
- CLEP Scoring System: Passing Scores & Raw vs. Scaled Score
- Continuing Education Opportunities for Molecular Biology Technologists
- WV College & Career Readiness Standards for Social Studies
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks

- Required Rate of Return (RRR): Formula & Calculation
- Fixed Phrases: Definition, Examples & Practice
- Why Do Workers Join Unions? - Benefits & Reasons
- Rigid Motion in Geometry
- Malabsorption Disorders & Energy Deficiencies
- Projectile Motion Experiment
- Professional Organizations & Literature for Media Specialists
- History of Wat Rong Khun
- Quiz & Worksheet - Animal Population Size
- Quiz & Worksheet - Psychoanalyst Anna Freud
- Quiz & Worksheet - Potassium Chromate
- Quiz & Worksheet - Understsanding Transaction Processing Systems
- Quiz & Worksheet - Decomposing Numbers
- Tourism Marketing Flashcards
- Tourism Economics Flashcards

- Educational Psychology: Homework Help Resource
- AP Macroeconomics: Homeschool Curriculum
- CBEST Writing: Practice & Study Guide
- Earth Science: Homework Help Resource
- High School Biology: Homeschool Curriculum
- McDougal Littell The Americans Chapter 8: Life at the Turn of the Century
- Holt McDougal Literature Chapter 1: Narrative Structure
- Quiz & Worksheet - Continuity & Differentiability
- Quiz & Worksheet - Fistula Characteristics & Treatment
- Quiz & Worksheet - Mitochondrion
- Quiz & Worksheet - Demand, Cost & Inventory Management
- Quiz & Worksheet - Pros & Cons of Small vs Large Lots

- Pinocytosis: Definition & Examples
- PTSD Assessment: Tools, Questionnaire & Scale
- Arizona Science Standards for High School
- Dolch Sight Words for Fourth Grade
- Homeschooling in Michigan
- North Dakota State Standards for Math
- Korean War Lesson Plan
- In-School Resources for Teacher Professional Development
- Subject-Verb Agreement Lesson Plan
- Best Apps for the Classroom
- Homeschooling in Ohio
- What Is the Syllabus of an Algebra I Course?

Browse by subject