Elementary Statistics (1+1)

8.2.1 Kurtosis

If we know the measures of central tendency, dispersion and skewness, we still cannot form a complete idea about the distribution as will be clear from the above figure in which all the three curves A, B and C are symmetrical about the mean ‘m’ and have the same range.

In addition to these measures we should know one more measure which Prof. Karl Pearson calls as the Convexity of a curve or Kurtosis. Kurtosis enables us to have an idea about the flatness or peakedness of the curve. It is measured by the co-efficient b ₂ or its derivation g ₂ given by

b ₂ = m ₄ / m ₂ ² g _{2 =} b ₂ – 3

Curve of the type ‘A’ which is neither flat nor peaked is called the normal curve or mesokurtic curve and for such a curve b ₂ = 3 i.e. g ₂ =0. Curve of the type ‘B’ which is flatter than the normal curve is known as platykurtic and for such a curve b ₂ < 3, i.e. g ₂ <0. Curve of the type ‘C’ which is more peaked than the normal curve is called leptokurtic and for such a curve b ₂ > 3 i.e. g ₂ >0.