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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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**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**• Range = (Maximum entry) – (Minimum entry) • Find range of the starting salaries (1000 of $): 41 38 39 45 47 41 44 41 37 42**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**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**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**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**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)**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation N = 10 σ² = SSx/N**Find mean, deviation, sum of squares, population variance &**std. deviation N = 10 σ² = SSx/N σ²= 88.5/10 = 8.85 σ= √σ²**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**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation**Find mean, deviation, sum of squares, population variance &**std. deviation N=10**Find mean, deviation, sum of squares, population variance &**std. deviation N=10 σ²=SSx/10**Find mean, deviation, sum of squares, population variance &**std. deviation N=10 σ²=SSx/10 σ²=1102.5/10 = 110.25**Find mean, deviation, sum of squares, population variance &**std. deviation N=10 σ²=SSx/10 σ²=1102.5/10 = 110.25 σ=√σ²**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**Find the SampleVariance and Sample Standard Deviation**n = 10**Find the Sample Variance and Sample Standard Deviation**n = 10 s²=SSx/(n-1)**Find the SampleVariance and Sample Standard Deviation**n = 10 s²=SSx/(n-1) s²=88.5/(10-1) = 88.5/9 =9.83**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**Find the Sample Variance and Sample Standard Deviation**n=10 s²=SSx/(n-1)**Find the Sample Variance and Sample Standard Deviation**n=10 s²=SSx/(n-1) s²=1102.5/(10-1) = 1102.5/9 = 122.5**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**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**Interpreting Standard Deviation**x=5 s=1.2 x=5 s=0 x=5 s=3.0**Estimate the Standard Deviation**N=8 µ=4 σ= N=8 µ=4 σ= N=8 µ=4 σ=**Estimate the Standard Deviation**N=8 µ=4 σ=0 N=8 µ=4 σ= N=8 µ=4 σ=**Estimate the Standard Deviation**N=8 µ=4 σ=0 N=8 µ=4 σ=1 N=8 µ=4 σ=+ 1 & 3**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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