1. Standardized variable:
The variable which measures the deviation from
mean in unit of standard deviation is called
standardized variable. The standardized variable is
independent of unit used. The mean of
standardized variable is equal to zero and variance
of standardized variable is equal to one.
10. Skewness:
The lack of symmetry in a distribution around
some central value i-e mean, median or mode or
the degree of asymmetry is called skewness.
Skewness may be positive or negative.
1. If the frequency curve has a longer tail to the
right of the distribution, is said to be positively
skewed.
2. If the frequency curve has a longer tail to the left
of the distribution is said to be negatively
skewed.
11. The difference between the mean and the mode
gives an absolute measure of skewness, if we
divide this difference by standard deviation, we
get a relative measure of skewness.
Coefficient of Skewness = Mean – Mode / Standard
deviation
or
Coefficient of Skewness = 3( Mean – Median) /
Standard deviation
Positive results for positively skewed distribution
and negative results for negatively skewed
distribution. For symmetrical distribution, this
measure will be zero.
13. Kurtosis:
Kurtosis is the degree of peakedness of a
distribution or flatness of a unimodal frequency
curve.
1. A distribution having a relatively high peak is
called leptokurtic.
2. A distribution which is flat topped is called
platykurtic.
3. The normal distribution that is neither very
peaked nor very flat topped is called mesokurtic.
Karl Pearson introduced the term kurtosis.