Lecture Slides 4.pptx

20 de Aug de 2022
1 de 14

Lecture Slides 4.pptx

• 1.  Standardized variable: The variable which measures the deviation from mean in unit of standard deviation is called standardized variable. The standardized variable is independent of unit used. The mean of standardized variable is equal to zero and variance of standardized variable is equal to one.
• 10.  Skewness: The lack of symmetry in a distribution around some central value i-e mean, median or mode or the degree of asymmetry is called skewness. Skewness may be positive or negative. 1. If the frequency curve has a longer tail to the right of the distribution, is said to be positively skewed. 2. If the frequency curve has a longer tail to the left of the distribution is said to be negatively skewed.
• 11.  The difference between the mean and the mode gives an absolute measure of skewness, if we divide this difference by standard deviation, we get a relative measure of skewness. Coefficient of Skewness = Mean – Mode / Standard deviation or Coefficient of Skewness = 3( Mean – Median) / Standard deviation Positive results for positively skewed distribution and negative results for negatively skewed distribution. For symmetrical distribution, this measure will be zero.
• 13.  Kurtosis: Kurtosis is the degree of peakedness of a distribution or flatness of a unimodal frequency curve. 1. A distribution having a relatively high peak is called leptokurtic. 2. A distribution which is flat topped is called platykurtic. 3. The normal distribution that is neither very peaked nor very flat topped is called mesokurtic. Karl Pearson introduced the term kurtosis.