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Understanding the Central Limit Theorem and Normal Distribution in Statistics

Explore the Central Limit Theorem and its implications in statistics. This lesson covers key concepts including numerical summaries like the mean and median, and measures of spread such as standard deviation and interquartile range. Learn how to apply these principles to sample proportions, understanding that with a large enough sample size, distributions will approximate normality. Additionally, delve into probability calculations related to normal distribution and interpret frequency data from real-world examples, including potassium levels and student scores.

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Understanding the Central Limit Theorem and Normal Distribution in Statistics

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Presentation Transcript

  1. Stat 217 – Day 8 Central Limit Theorem, cont.

  2. Last Time – Quantitative Data • Numerical summaries • center: mean vs. median • spread: standard deviation, interquartile range • BPS 1.47 – Which is the mean? • BPS 1.49 – Standard deviation game

  3. mean sd sd Last Time – Normal Distribution • Symmetric, bell-shaped curve with mean m and standard deviation s applet

  4. Last Time – Normal Probability z = 3.5-3.7 = 1.00 .2 Table A: prob below = .1587 About 16% of days the potassium level will read less than 3.5 meg/l

  5. Next • Apply these ideas to the Central Limit Theorem If n is large (np>10 and n(1-p)>10) then the distribution of sample proportions will be normal with mean p and standard deviation

  6. Last Time – Normal Probability Fisher: z = 90-75 = 2.14 7 Table A: 1- .9838 =.0162 About 1-2% of students receive score above 90

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