2.4-MEASURES OF VARIATION

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# 2.4-MEASURES OF VARIATION - PowerPoint PPT Presentation

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
• 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)

N = 10

σ² = SSx/N

N = 10

σ² = SSx/N

σ²= 88.5/10

= 8.85

σ= √σ²

N = 10

σ² = SSx/N

σ²= 88.5/10

= 8.85

σ= √σ²

σ =√8.85 = 2.97

N=10

N=10

σ²=SSx/10

N=10

σ²=SSx/10

σ²=1102.5/10

= 110.25

N=10

σ²=SSx/10

σ²=1102.5/10

= 110.25

σ=√σ²

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

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)

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=