meeting 07 Dispersion Skewness and Kurtosis

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3/26/2011

1 Dispersion, Skewness and

Kurt osis

Presen ted by: Mahen dra AN

Sources:

http:/ / busin ess.clayton .edu/ arjom an d/ busin ess/ stat%20 presen tation s/ busa310 1.htm l

Djarwan to, S ta tis tik S o s ia l Eko n o m iBagian pertam a edisi 3, BPFE, 20 0 1

Framework

Frequency distribution characteristics

Dispersion

_•_{Dispersion is separate}

m easures of values am on g its cen tral

Absolut e Dispersion

Ra n ge

•Sim plest dispersion m easure

•Effected by extrem e values

Qu a rtile D e via tio n

•Dispersion of in ter quartile ran ge

Absolut e Dispersion (cont . )

P e rce n tile D e via tio n

•Dispersion of in ter percen tile ran ge (P10an d

P90) P90)

Ave ra ge d e via tio n ( m e a n d e via tio n )

• Un grouped data

•Grouped data

Absolut e Dispersion (cont . )

S ta n d a rd d e via tio n

•Un grouped data

•Grouped data

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St andard Unit s

•To com pare two or m ore distribution s

•Stan dard un it show deviation of a variable value (X) on m ean ( ) in stan dard deviation un it (s) (X) on m ean ( ) in stan dard deviation un it (s)

•Com m on ly base on zero value (Z=0 )

•Exam ple: Z=1.2 is better than z=1.0

Relat ive Dispersion

•To kn ow sm allest variation in a distribution

•To com pare two or m ore frequen cy distribution

•All of stan dard dispersion m easurem en t can be

•All of stan dard dispersion m easurem en t can be used.

•Stated in coefficien t of variation

Skewness

•An im portan t m easure of the shape of a distribution is called skewn ess

•The form ula for com putin g skewn ess for a data

•The form ula for com putin g skewn ess for a data set is som ewhat com plex

Skewness (cont . )

Ka rl P e a rs o n m e th o d

•Base on m ean an d m edian values

B o w le y m e th o d

•Base on quartile values

Skewness (cont . )

10 – 9 0 p e rc e n tile 's m e th o d

•Base on percen tile

•The better m easurem en t for skewn ess base on the third m om en t.

Skewness (cont . )

•Grouped data skewn ess

•Third m om en t m ethod is used

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Distribution Shape:

Distribution Shape: SkewnessSkewness

SymmetricSymmetric((not skewed, SK = 0not skewed, SK = 0)) •

•If skewness is zero, thenIf skewness is zero, then

•

•Mean and median are equal.Mean and median are equal.

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Distribution Shape:

Moderately Skewed LeftModerately Skewed Left •

•Is skewness is negative Is skewness is negative (left skewed SK >= (left skewed SK >= --3),3),thenthen

•

•Mean will usually be less than the median.Mean will usually be less than the median.

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Distribution Shape:

Moderately Skewed RightModerately Skewed Right •

•If skewness is positive If skewness is positive (right skewed, SK >= +3),(right skewed, SK >= +3),thenthen

•

•Mean will usually be more than the median.Mean will usually be more than the median.

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Distribution Shape:

Highly Skewed RightHighly Skewed Right •

•Skewness is positive (often above 1.0).Skewness is positive (often above 1.0).

•

•Mean will usually be more than the median.Mean will usually be more than the median.

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•Measurem en t of peakedn ess

•Difficult to in terpret

•On ly in theoretic n ot in practice

Leptokurtic Mesokurtic

Plakurtic