What
is Skewness? Explain the factors causing divergence in normal
distribution. 2+ 4
Skewness:
Skewness is the degree of asymmetry of the distribution. A distribution is said
to be “skewed” when the mean and median do not coincide and the center of
gravity of the data is shifted to one side (left or right). In a normal
distribution the mean equals, the median exactly and the skewness is of course
zero (SK = 0).
There are two types of
skewness which appear in the normal curve
a) Negative
Skewness: Distribution said to be negatively skewed or left-skewed
when scores are concentrated on the higher end of the scale, i.e. the right
side of the curve are spread out more gradually toward the low end i.e. the
left side of the curve. In negatively skewed distribution the value of median
will be higher than that of the value of the mean.
b) Positive Skewness: Distributions are skewed positively or to the right, when scores are massed at the low; i.e. the left end of the scale, and are spread out gradually toward the high or right end as shown in the fig.
Divergence in normal distribution
Kurtosis: Kurtosis refers to the sharpness or
flatness of the peak of a distribution curve compared to a normal distribution.
It helps describe the shape of the
distribution, especially in the tails and peak. There are two types of
divergence in the peakness of the curve
a) Leptokurtosis:
Suppose there is a normal curve which is made up of a steel wire. If we push
both the ends of the wire curve together the curve become more peeked i.e. its
top become more narrow than the normal curve and scatterdness in the scores or
area of the curve shrink towards the center.
Thus
in a Leptokurtic distribution, the frequency distribution curve is more peaked
than to the normal distribution curve. The scores are less spread out, and
there are more data points near the mean.
Fig: Kurtosis in the Normal Curve
b) Platykurtosis:
Now suppose we put a heavy pressure on the top of the wire made normal curve the
curve become more flat than to the normal. Thus, a distribution of flatter Peak
than to the normal is known Platykurtosis distribution.
c) Mesokurtic:
The normal curve is said to be mesokurtic.