Descriptive StatisticsDescriptive Statistics

Measures of Skewness & KurtosisMeasures of Skewness & Kurtosis

Descriptive StatisticsDescriptive Statistics Measures of Central Tendency

• Mo• Mdn.• Mean

Measures of Variability• Range• Semi-Interquartile Range• Average Deviation• Standard Deviation

Measures of Skewness & Kurtosis

Skewness: Negative Skewness

0102030405060708090

Skewness: Positive Skewness

0102030405060708090100

Descriptive StatisticsDescriptive Statistics

0246810121416

Q2Q1 Q3

Measures based on Quartiles• Q3-Q2< Q2-Q1=Neg

skewness• Q3-Q2> Q2-Q1=Pos

Skewness• Pearsonian Measure of

Skewness

SkQQ Q Q

Q Q

1 3 2

3 1

2

+1 Pos 0 Norm -1 Neg

Measures of SkewnessMeasures of Skewness Measures based upon the third

moment around the Mean.A Moment is a

Deviation Score

Raised to some

POWER

X x x2 x3 x4

2 -4 16 -64 2564 -2 4 -8 167 1 1 1 18 2 4 8 169 3 9 27 81

0 34 -36 370

Measures of SkewnessMeasures of Skewness Measures based upon the third

moment around the Mean.

X x x2 x3 x4

2 -4 16 -64 2564 -2 4 -8 167 1 1 1 18 2 4 8 169 3 9 27 81

0 34 -36 3701

0 xN

2

22 x

N

3

3

xN

skewness

ig

3

365

345

3452 2

-1 Negative 0 Normal +1 Positive

Descriptive StatisticsDescriptive Statistics Measures of Skewness

• Pearsonian Measure of Skewness• Measures Based on 3rd Quartile

Measures of Kurtosis• Kurtosis is a measure of the flatness or peakedness of a

Distribution– Normal Kurtosis - Mesokurtic– Flat Kurtosis - Platokurtic– Peaked Kurtosis - Leptokurtic

• A Measure of Kurtosis based on the 4th moment about the Mean

24

2

2

2 3g

If less then 0 = PlatokurticMore than 0 = LeptokurticIf 0 then = Mesokurtic

Descriptive StatisticsDescriptive Statistics

The first test will cover material up to this point!!

14-Feb-97