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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
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
  • Range = (Maximum entry) – (Minimum entry)
  • Find range of the starting salaries (1000 of $):

41 38 39 45 47 41 44 41 37 42

range1
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

range2
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

range3
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

range4
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
  • 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 deviation11
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 deviation12
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 deviation24
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 deviation25
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 deviation26
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 sample v ariance and sample standard d eviation2
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 sample v ariance and sample standard d eviation3
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 deviation2
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 deviation3
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 deviation4
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
Interpreting Standard Deviation

x=5

s=1.2

x=5

s=0

x=5

s=3.0

estimate the standard deviation
Estimate the Standard Deviation

N=8

µ=4

σ=

N=8

µ=4

σ=

N=8

µ=4

σ=

estimate the standard deviation1
Estimate the Standard Deviation

N=8

µ=4

σ=0

N=8

µ=4

σ=

N=8

µ=4

σ=

estimate the standard deviation2
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 deviation3
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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