Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Skewness The coefficient of Skewness is a measure for the degree of symmetry in the variable distribution. Negatively skewed distribution or Skewed to the left Skewness <0 Normal distribution Symmetrical Skewness = 0 Positively skewed distribution or Skewed to the right Skewness > 0 Skewness is important because it affects the measure of central tendency we use to describe the data in the distribution. Consider these points: •In a negatively skewed distribution, the mean is less than the median- in certain circumstances, the median is a more appropriate description of the central tendency of the sample than the mean. •In a positively skewed distribution, the mean is greater than the median- in certain circumstances, the median is a more appropriate appropriate description of the central tendency of the sample than the mean. •In a normal distribution, the mean, median, and mode are all the same- while this can be convenient for describing the central tendency of the sample, it RARELY happens and so we can dismiss this is a relatively rare occurrence. Skewness and Measures of Central Tendency In a symmetrical distribution, the mean, median, and mode are all the same number. In a negatively skewed distribution, the mean is the smallest number; the mode is the largest number; the median is between the mean and mode. In a positively skewed distribution, the mean is the largest number; the mode is the smallest number; the median is between the mean and mode. Kurtosis The coefficient of Kurtosis is a measure for the degree of peakedness/flatness in the variable distribution. Platykurtic distribution Low degree of peakedness Kurtosis <0 Normal distribution Mesokurtic distribution Kurtosis = 0 Leptokurtic distribution High degree of peakedness Kurtosis > 0 Kurtosis is important because it affects the measure of dispersion we use to describe the data in the distribution. It does not directly affect the measure of dispersion we use, but we should note that: •In a platykurtic or flat distribution, the variance and standard deviation will be greater than in a normal or leptokurtic distribution; this means that there is more dispersion or variability in a platykurtic distribution than in either of the other shapes. •In a leptokurtic distribution or peaked distribution, the variance and standard deviation will be less than in a normal or platykurtic distribution; this means that there is less dispersion or variability in a leptokurtic distribution than in either of the other shapes. •In a normal distribution, the variance and standard deviation will be between those figures for a platykurtic or leptokurtic distribution;l such a distribution RARELY happens and so we can dismiss this is a relatively rare occurrence. Kurtosis and Measures of Dispersion | | | | | | | | 3 2 1 Mean 1 Most peaked curve Smallest dispersion Symmetrical curve Standard dispersion Flattest curve Widest dispersion 2 3