Measures of Skewness and Measures of Kurtosis

 

Measures of Skewness

    To say, skewness means 'lack of symmetry'. We study skewness to have an idea about the shape of the curve which we can draw with the help of the given data. A distribution is said to be skewed if Mean is not equals to Median is not equal to Mode. 

    If the left tail of the frequency curve is more elongated than right tail, it is known as negative skewness otherwise it as positive skewness.

    They are various measures of skewness are:

    Where M is the mean, Md is the Median, M0 is the Mode of the distribution. These are the absolute measures of skewness. As in dispersion, for comparing two series we do not calculate these absolute measures, but we calculate the relative measures called the coefficients of skewness which are pure numbers independent of units of measurements.

Measures of Kurtosis

    Kurtosis enables us to have an idea about the 'flatness or peakedness' of the frequency curve. It is measured by the coefficient beta suffix 2 or its derivation gamma suffix 2 given by

    Curve of the type 1 which is neither flat nor peaked is called the normal curve or mesokurtic curve and for such curve beta equals to three and gamma equals to zero.

    Curve of the type 2 which is flatter than the normal curve is called the platykurtic curve as beta less than three and gamma less than zero.

    Curve of the type 3 which is more peaked than the normal curve is called the leptokurtic curve as beta greater than three and gamma greater than zero.