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# 2.4-MEASURES OF VARIATION

2.4-MEASURES OF VARIATION. 1) Range – Difference between max &amp; min 2) Deviation – Difference between entry &amp; 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 N = 10 σ² = SSx/N

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

10. 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

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

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

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

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

15. 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

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

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

18. 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

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

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

21. 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

22. 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

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

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

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

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

27. 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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