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8/9/2019 Take 9 - Skewness, Kurtosis, Boxplot
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SKEWNESS, KURTOSIS,
BOXPLOTDESCRIBING SHAPES AND PATTERNS
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SKEWNESSSymmetry of Distribution
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MOTIVATION:
In both histograms, the mean is 6 and the
variance is roughly around 8.7. But, the shape
of distribution of values are not necessarily thesame. Hence, the measures of skewness and
kurtosis are summary measures that describe
the shape of the distribution.
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SKEWNESS
• A measure of symmetry/asymmetry of a
distribution of values in a data.
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SKEWNESS
POSITIVELY SKEWED or SKEWED TOTHE RIGHT - the concentration of the
values are on the left side of the distribution,
with a tail that is tapering off on the right
side.
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SKEWNESS
NEGATIVELY SKEWED or SKEWED TOTHE LEFT - the concentration of the values
are on the right side of the distribution, with
a tail that is tapering off on the left side.
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SKEWNESS
• the distribution is symmetric, if the mean =
median = mode.
• the distribution is skewed to the right or
positively skewed, if the mean > median >
mode.
• the distribution is skewed to the left or
negatively skewed, if the mean < median <
mode.
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SKEWNESS
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SKEWNESS
′
1 −
′
2 −
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SKEWNESS
Interpretation:if the coefficient of skewness is less than 0,
then the distribution is skewed to the left or
negatively skewed.
If the coefficient of skewness is greaterthan 0, then the distribution is skewed to
the right or positively skewed.
If the coefficient of skeweness is 0, then the
distribution is symmetric.
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KURTOSISConcavity of Distribution
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KURTOSIS
• It describes the “hump” of the
distribution of the values relative to
the “hump” of a normal distribution of
the same amount of variability.
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KURTOSIS
• The Normal Distribution:
– It is a bell-shaped curve.
– It is symmetric about its mean.
– It has tails that extend on both ends but it doesn’ttouch the x-axis
– The area below the curve and above the x-axis is 1.
– 68% of observations lie within one standard deviation
from the mean, 95% of observations lie within twostandard deviations from the mean, and at least 99%
of observations lie within three standard deviations
from the mean.
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KURTOSIS
• The Normal Distribution
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KURTOSIS
• Coefficient of kurtosis:
4
4
=1
4
4
interpretation:4
4 3 < 0 →
4
4 3 > 0 → 4
4 3 0 →
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KURTOSIS
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KURTOSIS
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BOXPLOTExploratory-Data-Analysis Tool
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BOXPLOT
Box-and-whisker plot – a
graphical tool for assessing
the shape of distribution.Features:
Location
Spread
Symmetry
Extremes
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BOXPLOT
OUTLIERS!
3rd Quartile
1st Quartile
2nd Quartile
Or Mean
AXIS
Q3+1.5(IQR)
or max
Q1-1.5(IQR)
or min
Range of
the
middle50% of
the data
IQR=Q3-Q1
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ASSESSING SKEWNESS
USING A BOXPLOT
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DESCRIBE THE SKEWNESS
OF EACH BOXPLOT
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/:END:/