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God Teaches the Lesson of the Sample Mean

God Teaches the Lesson of the Sample Mean. Squared Error. Which Squared Error?. Measuring Best. minimize. Calculati Form a Plan. Algebrati Form a Plan. Vertex of y = ax 2 + bx + c is at x = -b/(2a). Calculati Compute the Derivative. Calculati Set the Derivative to Zero.

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God Teaches the Lesson of the Sample Mean

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  1. God Teaches the Lesson of the Sample Mean

  2. Squared Error

  3. Which Squared Error?

  4. Measuring Best minimize

  5. Calculati Form a Plan

  6. Algebrati Form a Plan • Vertex of y = ax2 + bx + c • is at x = -b/(2a)

  7. Calculati Compute the Derivative

  8. Calculati Set the Derivative to Zero

  9. Calculati Find Best Representative • (x1+x2+x3)/3

  10. The Lesson of Uncertainty • Three Scientists Receive Three Samples

  11. Mean for Scientist One

  12. Means for Scientists Two and Three

  13. Algebraists to the Fore • Compare Three Sample Means With the Population Mean

  14. The Mean of the Sample Means is the Population Mean • End of Act One

  15. God Teaches the Mystery of n-1

  16. Least Squared Error • SSE = (x1-)2 + (x2-)2 + (x3-)2 . . . until the end of the Population

  17. God Challenges Man Again

  18. Scientist One’s Plan

  19. Scientist Two’s Plan • Guess = 3/2 Times SSE of Sample

  20. The First Practice Test • And the first practice test was {12, 12, 0}. • the three Samples would be {12,12}, {12,0}, and {12,0}.

  21. First Practice Test • From this generation of answers was begat the three Sample SSE values

  22. Strategy of Scientist One • SSE guesses as 0, 72 and 72.

  23. Multiply-by-3/2 strategy Recommended by Scientist Two • the three guesses as 0, 108 and 108

  24. Computations for God and the SSE of the Population Then God would compute the mean of their guesses as (0 +72+72)/3 = 48 for the Scientist One strategy and (0+108+108)/3 = 72 for the Scientist Two strategy.

  25. More Practice Tests

  26. Sacred Relics • The URL for the proof is • http://www.mr-ideahamster.com/stat-think/n-minus-one.pdf • Excel Spreadsheet • http://www.mr-ideahamster.com/stat-think/nm1study.xls

  27. Scaling N=6 • N n scale factor • 3 2 2/1 • 6 5 5/4 • 6 4 5/3 • 6 3 5/2 • 6 2 5/1

  28. Normalize by n-1 • General Scale Factor is (N-1)/(n-1) • Use SSE/(n-1) Eliminates all scale factors • SSE/(n-1) is called the Variance

  29. Go Forth and Nevermore ask Why Divide by n-1

  30. The End

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