These are my skewness notes for S1 which explain the coefficient of skewness at the bottom.
In a symmetrical distribution mean = median = mode and Q2 – Q1 = Q3 – Q2. A positive skew distribution has a tail to the positive side, mean > median > mode and Q2 – Q1 < Q3 – Q2. A negative skew distribution has a tail to the negative side, mean < median < mode and Q2 – Q1 > Q3 – Q2. Skewness can be given quantity as well as direction by using (3 (mean-median))/(standard deviation) . To compare the relative dispersion between data sets the coefficient of variation is used, it is given by V= 100σ/μ= 100s/x ̅ and as a percentage. When data is skewed the median and the interquartile range are used as measures of location and dispersion as they are not affected by extreme values. The dispersion of a set of data is therefore measured by the quartile coefficient of variation which is given by QV= (50 (Q_3- Q_1))/Q_2 .
x ̅ is mean of x and Q_3 is the upper quartile mark, if the notation wasnt that clear
Last edited by abbii; 18-04-2010 at 21:29.
Last edited by .ACS.; 18-04-2010 at 21:35.
Reason: Decided to add Latex