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skewness of normal distribution curve.....
1. DIVERGENCE IN NORMALITY
Two types of divergence in normal probability curve. They are-
1) Skewness-Skewness is a measure of the asymmetry of a
distribution
2) Kurtosis-Kurtosis is a measure of the tailedness of a distribution.
(outliers)
2. SKEWNESS
A distribution is said to be skewed when the mean and the
median fall at different points in the distribution, and the
balance (or centre of gravity) is shifted to one side or the
other- to left or right.
Measures of skewness tell us the direction and the extent
of skewness. In symmetrical distribution the mean, median
and mode are identical. The more mean moves away from
the mode, the larger the asymmetry or skewness.
4. POSITIVELY SKEWED
ALSO KNOWN AS RIGHT SKEWED DISTRIBUTION.
MEAN> MEDIAN> MODE
THE RIGHT TAIL OF THE CURVE IS LONGER THAN ITS LEFT TAIL WHEN THE DATA IS PLOTTED
ON A GRAPH
5. NEGATIVELY SKEWED
ALSO KNOWN AS LEFT SKEWD DISTRIBUTION.
MEAN< MEDIAN< MODE
THE LEFT TAIL OF THE CURVE IS LONGER THAN ITS RIGHT TAIL WHEN THE DATA IS PLOTTED ON A
GRAPH
6. NEGATIVE
SKEWNESS
The left tail is longer, the mass of the
distribution is concentrated on the right of
the figure.
Long tail in the negative direction on the
number line.
The mean is also the left of the peak.
POSITIVE SKEWNESS
The right tail is longer; the mass of the
distribution is concentrated on the left
of the figure.
Long tail in the positive direction on the
number line.
The mean is also right of the peak.
7. KURTOSIS
In probability theory and statistics, kurtosis is a measure that
tells us whether the data is heavy tailed or light tailed in a
normal distribution.
Kurtosis tells us about the peakness or flatness of the
distribution. Kurtosis is basically the statistical measure that
helps to identify the data around the mean.
8. TYPES OF KURTOSIS
Leptokurtic or heavy tailed distribution (kurtosis more than
normal distribution)
Mesokurtic (kurtosis same as the normal distribution0
Platykurtic or short tailed distribution (kurtosis less than
normal distribution)
9. LEPTOKURTIC
Leptokurtic is having very long and
skinny tails, which means there are
more chances of outliers.
Positive values of kurtosis indicate
that distribution is peaked and
possess thick tails.
10. PLATYKURTIC
Platykurtic having a lower tail and stretched
around the centre tail means most of the data
points are present in high proximity with mean.
A platykurtic distribution is flatter (less peaked)
when compared with normal distribution.
11. MESOKURTIC
Mesokurtic is the same as the
normal distribution, which
means kurtosis is near to 0.
In mesokurtic, distributions are
normal in breadth and curves
are a medium peaked height.
Editor's Notes
A distribution can have right (or positive), left (or negative), or zero skewness
Normal distributions have zero skew, but they’re not the only distributions with zero skew. Any symmetrical distribution, such as a uniform distribution or some bimodal (two-peak) distributions, will also have zero skew.
The distribution of scores on any particularly difficult exam will be positively skewed with most students scoring around some mean value with a few outlstanding students scoring much higher.
The distribution of the age of deaths in most populations is negatively skewed. Most people live to be between 70 and 80 years old, with fewer and fewer living less than this age.
