Difference between revisions of "Central Limit Theorem"
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The random variable <math>\bar{X}</math> has a different z-score associated with it than the random variable <math>X</math>. <math>\bar{x}</math> is the value of <math>\bar{X}</math> in one sample. | The random variable <math>\bar{X}</math> has a different z-score associated with it than the random variable <math>X</math>. <math>\bar{x}</math> is the value of <math>\bar{X}</math> in one sample. | ||
| − | <math> | + | <math>z=\frac{\bar{x}-\mu_x}{\left (\frac{\sigma_X}{\sqrt{n}} \right )}</math> |
<math>\mu_x</math> is both the average of <math>X</math> and <math>\bar{X}</math> | <math>\mu_x</math> is both the average of <math>X</math> and <math>\bar{X}</math> | ||
<math>\Huge\frac{\sigma_X}{\sqrt{n}}</math> is the standard deviation of <math>X</math> and is called the '''[[Standard error|Standard error]]'''. | <math>\Huge\frac{\sigma_X}{\sqrt{n}}</math> is the standard deviation of <math>X</math> and is called the '''[[Standard error|Standard error]]'''. | ||
Latest revision as of 19:54, 27 August 2020
The Central Limit Theorem for Sample Means (Averages) says that if you keep drawing larger and larger samples (like rolling 1, 2, 5, and, finally, 10 dice) and calculating their mean tthe sample means (averages) form their own normal distribution (the sampling distribution). The normal distribution has the same mean as the original distribution and a variance that equals the original variance divided by <n>, the sample size. <n> is the number of values that are averaged together not the number of times the experiment is done.
The random variable has a different z-score associated with it than the random variable . is the value of in one sample. is both the average of and Failed to parse (unknown function "\Huge"): {\displaystyle \Huge\frac{\sigma_X}{\sqrt{n}}} is the standard deviation of and is called the Standard error.
Part of: M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals
See also: http://en.wikipedia.org/wiki/Central_limit_theorem
