09 Measures of Variability

8/13/2019 09 Measures of Variability

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Measures of

Variability


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Sets of grades in Statistics of two sections

Wisdom Faith

Mark: 82 Hero: 70

Jennylyn: 80 Sandara: 95

Rainier: 83 Joross: 60

Yasmien: 81 Roxanne: 80

Nadine: 79 Melissa: 100

Mean: 81 Mean: 81


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Measures of Variability or Dispersion

are measures of the average distance of eachobservation from the center of the distribution

they measure the homogeneity or heterogeneity

of a particular groupSeveral Measures of Variability or Dispersion

Range

Mean Absolute Deviation

Variance

Standard Deviation


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Measures of

Variability forUngrouped Data


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Range

is the difference between the highest andlowest values

the simplest but the most unreliable measureof variability since it uses only two values in

the distribution

vv L H R

Where: R = rangeHv = highest value

Lv = lowest value


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is the average of the summation of theabsolute deviation of each observation fromthe mean

N

X X MAD

Where: X = is a value or score from the raw data= is the mean

N = total number of observationX


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Variance

is the average of the squared deviation fromthe mean



N

X X

2

2

1

2

2

N

X X s

Population Variance:

Sample Variance:


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Standard Deviation

is the square root of the average deviationfrom the mean, or simply the square root ofvariance



N

X X

2

1

2

N

X X s

Population Standard

Deviation: Sample StandardDeviation:


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Coefficient of Variation

is the ratio of the standard deviation to themean

Where: cv = coefficient of variation= is the mean

s = standard deviationX

it is used to compare the variability of two ormore sets of data even when they are

expressed in different unit of measurement

X

s cv


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Measures of

Variability forGrouped Data


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Range

LLULR

Where: R = rangeUL = upper limit (highest class)LL = lower limit (lowest class)


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Where: X = is the class mark= is the mean

N = total number of observationf = frequency

X

N

X X f MAD


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Variance

Population Variance:

Sample Variance:

N

X X f 2

2

1

2

2

N

X X f s

Where: X = is the class mark= is the meanN = total number of observationf = frequency

X


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Standard Deviation

Population StandardDeviation:

Sample StandardDeviation:

Where: X = is the class mark= is the meanN = total number of observationf = frequency

X

N

X X f

2

1

2

N

X X f s


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TABLE I

Score Distribution of Students in Literature Quiz

CI f CBLCB UCB

Class Mark(x)

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09 Measures of Variability