Kurtosis & skewness

Skewness and Kurtosis AGB 111 Dept. of AGB Veterinary College, Hebbal

Skewness • Skewness helps us to study the shape. i.e symmetry or asymmetry of the distribution • It gives an idea of the shape of the curve which we can draw • It helps us to determine the nature and content of the concentration of the observations towards the higher or lower values of the variable. .

Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore

If longer tail is towards the right it is positively skewed If the longer tail is towards left it is negatively skewed.

Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore

Measures of skewness Skewness = Mean – Median or Skewness = Mean-Mode

Co-effcient of skewness Skewness = Mean- Mode SD By using Mode = 3Median -2 Mean

Sk = Mo-(3Median-2Mean) = 3(Mean- Median) Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore σ σ

Kurtosis • Kurtosis refers to flatness or peakedness

In the above curve all the three distribution are symmetrical with same range.

It gives an idea about the shape and nature of the hump (middle part) of a frequency distribution.

Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore

Relationship between mean, median and mode • In case of symmetrical (normal distribution) the mean, median and mode coincide. • For a moderately asymmetrical (non-symmetrical or skewed) distribution mean and mode usually lie on the two ends.

Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore

Location of Mean Median and Mode

Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore

Empirical relationship Mode= Mean – 3(Mean- median)

Mean- mode = 3(Mean- median) Mean- Median =1/3(Mean-Mode) Thus, we see that the difference between mean and mode is three times the difference between mean and median.

Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore

Negatively skewed distribution

Positively skewed M > Md> Mo

Mo> Md> M

Mean ±σ =68.27% Mean ±2σ =95.45% Mean ±3σ =99.73% Dr. R. Jayashree, Asst. Prof, Dept. Of AGB Veterinary College, Hebbal, Bangalore