Skewness (or Asymmetry)
It is a measure of how much the distribution is asymmetric.
𝑖^𝑡ℎ frequency density = Frequency per unit interval =𝑓_𝑖/ℎ.
Symmetric distribution: If a perpendicular is drawn on the X-axis, it divides the figure into two congruent parts i.e. identical in all respect or one part can be superimposed on the other i.e., mirror images of each other.
If the left tail and the right tail are equal, we get a symmetric distribution for which mean = median = mode.
Asymmetric distribution: If the right tail is longer, we get a positively skewed distribution for which mean greater than median, which is greater than mode.
If the left tail is longer, we get a negatively skewed distribution for which mean less than median, which is less than mode.
Median is always between Mean and Mode.
In negatively skewed distribution, among these three measures, Mean is the lowest while Mode is the highest value.
In positively skewed distribution, among these three measures, Mode is the lowest while Mean is the highest value.
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Difference between Variance and Skewness
Variance tells us about the amount of variability while skewness gives the direction of variability.
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Where do we need Variance?
In business and economic series, measures of variation have greater practical application than measures of skewness.
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Where do we need Skewness?
In medical and life science field measures of skewness have greater practical applications than the variance.
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Two measures of Skewness
1. Absolute 2. Relative
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Three criteria for a good measure of skewness
1. Should be independent of the underlying unit of the variables so that the symmetry of different distributions with different units can be compared.
2. If the distribution is symmetric, the value of the measure should be zero. Similarly, the measure should give positive or negative values according as the distribution has positive or negative skewness respectively.
3. As we move from extreme negative skewness to extreme positive skewness, the value of the measure should vary accordingly.
00:00 What is skewness or asymmetry?
02:24 Discrete frequency distribution
04:19 Continuous frequency distribution
05:16 What is Frequency density?
08:50 Frequency density of equal class intervals
11:38 Symmetric distribution
15:54 Positively skewed asymmetric distribution
19:29 Negatively skewed asymmetric distribution
22:03 Difference between Variance and Skewness
22:25 Criteria for good measure of skewness
24:02 Odd-ordered central moments
27:24 Absolute and Relative measures of skewness
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