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Shape of Data
 Shape of data is measured by
 Skewness
 Kurtosis
1
Skewness
 Measures asymmetry of data
 Positive or right skewed: Longer right tail
 Negative or left skewed: Longer left tail
2/3
1
2
1
3
21
)(
)(
Skewness
Then,ns.observatiobe,...,Let













n
i
i
n
i
i
n
xx
xxn
nxxx
2
Kurtosis
 Measures peakedness of the distribution of
data. The kurtosis of normal distribution is 0.
3
)(
)(
Kurtosis
Then,ns.observatiobe,...,Let
2
1
2
1
4
21














n
i
i
n
i
i
n
xx
xxn
nxxx
3

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Business statistics (Shape of data)

  • 1. Shape of Data  Shape of data is measured by  Skewness  Kurtosis 1
  • 2. Skewness  Measures asymmetry of data  Positive or right skewed: Longer right tail  Negative or left skewed: Longer left tail 2/3 1 2 1 3 21 )( )( Skewness Then,ns.observatiobe,...,Let              n i i n i i n xx xxn nxxx 2
  • 3. Kurtosis  Measures peakedness of the distribution of data. The kurtosis of normal distribution is 0. 3 )( )( Kurtosis Then,ns.observatiobe,...,Let 2 1 2 1 4 21               n i i n i i n xx xxn nxxx 3