Central Limit Theorem - Revision history

Dirkjan at 19:54, 27 August 2020

2020-08-27T19:54:09Z

Dirkjan at 19:18, 27 August 2020

2020-08-27T19:18:23Z

Dirkjan: Created page with "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 the..."

2020-08-25T07:57:55Z

Created page with "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 the..."

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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 <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>\Huge 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>\Huge\frac{\sigma_X}{\sqrt{n}}</math> is the standard deviation of <math>X</math> and is called the '''[[Standard error|Standard error]]'''.

Part of: [[M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals|M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals]]
See also: http://en.wikipedia.org/wiki/Central_limit_theorem
[[Category:mbi]]

[[Category:Decision]]

[[Category:M7]]

[[Category:Methods]]

[[Category:Quantitative]]

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← Older revision		Revision as of 19:18, 27 August 2020
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−	~~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.	+	Central Limit Theorem
−
−	~~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>\Huge 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>\Huge\frac{\sigma_X}{\sqrt{n}}</math> is the standard deviation of <math>X</math> and is called the '''[[Standard error\|Standard error]]'''.~~
−
−
−	~~Part of: [[M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals\|M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals]]~~
−	~~See also: http://en.wikipedia.org/wiki/Central_limit_theorem~~
	[[Category:mbi]]		[[Category:mbi]]

← Older revision		Revision as of 19:54, 27 August 2020
Line 1:		Line 1:
−	Central Limit Theorem	+	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 <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>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>\Huge\frac{\sigma_X}{\sqrt{n}}</math> is the standard deviation of <math>X</math> and is called the '''[[Standard error\|Standard error]]'''.
		+
		+
		+	Part of: [[M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals\|M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals]]
		+	See also: http://en.wikipedia.org/wiki/Central_limit_theorem
	[[Category:mbi]]		[[Category:mbi]]