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2.4-MEASURES OF VARIATION

2.4-MEASURES OF VARIATION. 1) Range – Difference between max & min 2) Deviation – Difference between entry & mean 3) Variance – Sum of differences between entries and mean, divided by population or sample -1. 4) Standard Deviation – Square root of variance. Range.

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2.4-MEASURES OF VARIATION

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  1. 2.4-MEASURES OF VARIATION • 1) Range – Difference between max & min • 2) Deviation – Difference between entry & mean • 3) Variance – Sum of differences between entries and mean, divided by population or sample -1. • 4) Standard Deviation – Square root of variance

  2. Range • Range = (Maximum entry) – (Minimum entry) • Find range of the starting salaries (1000 of $): 41 38 39 45 47 41 44 41 37 42

  3. Range • Range = (Maximum entry) – (Minimum entry) • Find range of the starting salaries (1000 of $): • 38 39 45 47 41 44 41 37 42 47-37 = range of 10 or $10,000

  4. Range • Range = (Maximum entry) – (Minimum entry) • Find range of the starting salaries (1000 of $): • 38 39 45 47 41 44 41 37 42 47-37 = range of 10 or $10,000 • Find range of the starting salaries (1000 of $): 40 23 41 50 49 32 41 29 52 58

  5. Range • Range = (Maximum entry) – (Minimum entry) • Find range of the starting salaries (1000 of $): • 38 39 45 47 41 44 41 37 42 47-37 = range of 10 or $10,000 • Find range of the starting salaries (1000 of $): 40 23 41 50 49 32 41 29 52 58

  6. Range • Range = (Maximum entry) – (Minimum entry) • Find range of the starting salaries (1000 of $): • 38 39 45 47 41 44 41 37 42 47-37 = range of 10 or $10,000 • Find range of the starting salaries (1000 of $): 40 23 41 50 49 32 41 29 52 58 58 – 23 = 35 or $35,000

  7. Deviation • Deviation = How far away entries are from mean. For each entry, entry – mean of data set. x = x - µ. May be positive or negative • Population Variance = Mean of the SQUARE of the variance. σ² = Σ(x-µ)²÷N • Sample Variance = Variance for a SAMPLE of a population. s² = Σ(x-x)²÷(n-1) • Standard deviation = SQUARE ROOT of variance. σ = √ Σ(x-µ)² ÷ Ns=√Σ(x-x)²÷(n-1)

  8. Find mean, deviation, sum of squares, population variance & std. deviation

  9. Find mean, deviation, sum of squares, population variance & std. deviation

  10. Find mean, deviation, sum of squares, population variance & std. deviation

  11. Find mean, deviation, sum of squares, population variance & std. deviation

  12. Find mean, deviation, sum of squares, population variance & std. deviation

  13. Find mean, deviation, sum of squares, population variance & std. deviation

  14. Find mean, deviation, sum of squares, population variance & std. deviation

  15. Find mean, deviation, sum of squares, population variance & std. deviation

  16. Find mean, deviation, sum of squares, population variance & std. deviation

  17. Find mean, deviation, sum of squares, population variance & std. deviation

  18. Find mean, deviation, sum of squares, population variance & std. deviation N = 10 σ² = SSx/N

  19. Find mean, deviation, sum of squares, population variance & std. deviation N = 10 σ² = SSx/N σ²= 88.5/10 = 8.85 σ= √σ²

  20. Find mean, deviation, sum of squares, population variance & std. deviation N = 10 σ² = SSx/N σ²= 88.5/10 = 8.85 σ= √σ² σ =√8.85 = 2.97

  21. Find mean, deviation, sum of squares, population variance & std. deviation

  22. Find mean, deviation, sum of squares, population variance & std. deviation

  23. Find mean, deviation, sum of squares, population variance & std. deviation

  24. Find mean, deviation, sum of squares, population variance & std. deviation

  25. Find mean, deviation, sum of squares, population variance & std. deviation

  26. Find mean, deviation, sum of squares, population variance & std. deviation

  27. Find mean, deviation, sum of squares, population variance & std. deviation

  28. Find mean, deviation, sum of squares, population variance & std. deviation

  29. Find mean, deviation, sum of squares, population variance & std. deviation

  30. Find mean, deviation, sum of squares, population variance & std. deviation N=10

  31. Find mean, deviation, sum of squares, population variance & std. deviation N=10 σ²=SSx/10

  32. Find mean, deviation, sum of squares, population variance & std. deviation N=10 σ²=SSx/10 σ²=1102.5/10 = 110.25

  33. Find mean, deviation, sum of squares, population variance & std. deviation N=10 σ²=SSx/10 σ²=1102.5/10 = 110.25 σ=√σ²

  34. Find mean, deviation, sum of squares, population variance & std. deviation N=10 σ²=SSx/10 σ²=1102.5/10 = 110.25 σ=√σ² σ=√110.25 = 10.5

  35. Find the SampleVariance and Sample Standard Deviation n = 10

  36. Find the Sample Variance and Sample Standard Deviation n = 10 s²=SSx/(n-1)

  37. Find the SampleVariance and Sample Standard Deviation n = 10 s²=SSx/(n-1) s²=88.5/(10-1) = 88.5/9 =9.83

  38. Find the SampleVariance and Sample Standard Deviation n = 10 s²=SSx/(n-1) s²=88.5/(10-1) = 88.5/9 =9.83 s=3.14

  39. Find the Sample Variance and Sample Standard Deviation n=10

  40. Find the Sample Variance and Sample Standard Deviation n=10 s²=SSx/(n-1)

  41. Find the Sample Variance and Sample Standard Deviation n=10 s²=SSx/(n-1) s²=1102.5/(10-1) = 1102.5/9 = 122.5

  42. Find the Sample Variance and Sample Standard Deviation n=10 s²=SSx/(n-1) s²=1102.5/(10-1) = 1102.5/9 = 122.5 s=√s²

  43. Find the Sample Variance and Sample Standard Deviation n=10 s²=SSx/(n-1) s²=1102.5/(10-1) = 1102.5/9 = 122.5 s=√s² s=√122.5 = 11.07

  44. Interpreting Standard Deviation x=5 s=1.2 x=5 s=0 x=5 s=3.0

  45. Estimate the Standard Deviation N=8 µ=4 σ= N=8 µ=4 σ= N=8 µ=4 σ=

  46. Estimate the Standard Deviation N=8 µ=4 σ=0 N=8 µ=4 σ= N=8 µ=4 σ=

  47. Estimate the Standard Deviation N=8 µ=4 σ=0 N=8 µ=4 σ=1 N=8 µ=4 σ=+ 1 & 3

  48. Estimate the Standard Deviation N=8 µ=4 σ=0 N=8 µ=4 σ=1 N=8 µ=4 σ=2 σ²=

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