Kurtosis is the statistical measure that tells us when a distribution is more or less peaked tahn a normal distribution.
Different formulae for measuring kurtosis are:
i) Moment coefficient of kurtosis
One measure of kurtosis uses the fourth moment about the mean expresses in dimensionless form:
which is often denoted as b2
ii) Excess kurtosis:
Kurtosis is more commonly defined as the fourth cumulant divided by the square of the second cumulant, which is equal to the fourth moment around the mean divided by the square of the variance minus 3,
iii) Percentile coefficient of kurtosis
Another measure of kurtosis is based on both quartiles and percentiles and is given by:
where is the semi-interquartile range.
The following frequency distribution indicates the test scores of 40 students in Educational Measurement and Evaluation. Calculate the coefficient of kurtosis.
SD = 7.22