Skewness

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Skewness and Kurtosis :

Skewness and Kurtosis K.Anusha Tvm/o9-03

SKEWNESS:

SKEWNESS Skewness is the degree of departure from symmetry of a distribution .

SYMMETRICAL DISTRIBUTION :

SYMMETRICAL DISTRIBUTION Mean ,median ,and mode coincides Skewness will be zero

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Positive skew : The right tail is longer; the mass of the distribution is concentrated on the left of the figure.mean will be greater than median. The distribution is said to be right-skewed or " skewed to the right ".

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Negative skew : The left tail is longer; the mass of the distribution is concentrated on the right of the figure.Median will be greater than mean. The distribution is said to be left-skewed or " skewed to the left

MEASURES OF SKEWNESS:

MEASURES OF SKEWNESS Direction & extent of skewness 1) Pearson’s measure of skewness 2) Bowley’s measure of skewness

Pearson’s measure of skewness:

Pearson’s measure of skewness Distance b/n mean & mode is the basis Skewness – measured to compare series Meaning of skewness differ with variation in distribution.

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Karl Pearson suggested simpler calculations as a measure of skewness The Pearson mode or first skewness coefficient, defined by: ( mean − mode ) / standard deviation , Pearson's median or second skewness coefficient defined by 3 ( mean − median ) / standard deviation . Range skewness: -3 to +3

Bowley’s measure of skewness:

Bowley’s measure of skewness SYMMETRIC Q 1 MEDIAN Q 3 Q1 MEDIAN Q3 Q1 MEDIAN Q3 RIGHT SKEWED LEFT SKEWED

SkB= Q3+Q1-2*MEDIAN Q3-Q1:

Sk B= Q 3 +Q 1 -2*MEDIAN Q 3 -Q 1 Sk B = Q 1 -2Q 2 +Q 3 Q 3 -Q 1 RANGE: -1 to+1 (OR)

KURTOSIS:

KURTOSIS Kurtosis is the degree of peakedness of a distribution . KURTOSIS: Greek – “bulginess ” Normal curve – mesokurtic “ of intermediate peakedness”

Platykurtic :

Platykurtic A description of the kurtosis in a distribution in which the statistical value is negative . When compared to a normal distribution, a platykurtic data set has a flatter peak around its mean, which causes thin tails within the distribution. The flatness results from the data being less concentrated around its mean, due to large variations within observations.

Leptokurtic :

Leptokurtic A description of the kurtosis in a distribution in which the statistical value is positive. Leptokurtic distributions have higher peaks around the mean compared to normal distributions, which leads to thick tails on both sides. These peaks result from the data being highly concentrated around the mean, due to lower variations within observations.

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Thanq

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