descriptive statistics measures of skewness & kurtosis
DESCRIPTION
Skewness: Negative SkewnessTRANSCRIPT
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