Skewness
and its Types
In probability theory and statistics, skewness is a measure of the asymmetry
of the probability distribution of a real-valued random
variable about its mean. The
skewness value can be positive or negative, or undefined. For a unimodal distribution, negative skew commonly indicates that the tail is
on the left side of the distribution, and positive skew indicates that the tail
is on the right. In cases where one tail is long but the other tail is fat,
skewness does not obey a simple rule. For example, a zero value means that the
tails on both sides of the mean balance out overall; this is the case for a
symmetric distribution, but can also be true for an asymmetric distribution
where one tail is long and thin, and the other is short but fat. Many textbooks
teach a rule of thumb stating that the mean is right of the median under right
skew, and left of the median under left skew. This rule fails with surprising
frequency. It can fail in multimodal distributions, or in distributions where
one tail is long but the other is heavy. Most commonly, though, the rule fails
in discrete distributions where the areas to the left and right of the median
are not equal.
Types of
skewness
Consider the two distributions
in the figure just below. Within each graph, the values on the right side of
the distribution taper differently from the values on the left side. These
tapering sides are called tails,
and they provide a visual means to determine which of the two kinds of skewness
a distribution has:
Negative
skew. The left tail is longer; the
mass of the distribution is concentrated on the right of the figure. The
distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact
that the curve itself appears to be skewed or leaning to the right; left instead refers to the left
tail being drawn out and, often, the mean being skewed to the left of a typical
center of the data. A left-skewed distribution usually appears as a right-leaning curve.
Positive
skew: The right tail is longer; the
mass of the distribution is concentrated on the left of the figure. The
distribution is said to be right-skewed, right-tailed, or skewed to the right, despite the fact that the curve
itself appears to be skewed or leaning to the left; right instead refers to the
right tail being drawn out and, often, the mean being skewed to the right of a
typical center of the data. A right-skewed distribution usually appears as
a left-leaning curve.
.svg)
Figure 1 shows positive and
negative skew
skewness,(sk) = 
= 3(M-MD)/SD
table1 shows
the difference between the mean, median and mode in distribution
If mean –mode>0(positive)
the distribution is skewed to the right or positively skewed
If mean –mode >0(negative)
the distribution is skewed to the left or negatively skewed
If mean –mode =0(symmetrical)
the distribution is symmetrical
