Skewness

Meaning of Skewness

• Measure of skewness gives the direction and the magnitude of the lack of symmetry.
• Lack of symmetry is called skewness for a frequency distribution.

Meaning of Skewness

• A distribution is called symmetric if mean, median and mode coincide.
• If the distribution is not symmetric, the frequencies will not be uniformly distributed about the centre of the distribution.

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Types of Skewness

Positively Skewed or Skewed to the Right Distribution�

• Distribution tapers more to the right than to the left
• has a longer tail to the right compared to a much

Shorter left tail

• values are more concentrated below than above the mean
• Large values in the right tail are not offset by correspondingly low values in the left tail and consequently the mean will be greater than the median�

Negatively Skewed or Skewed to the Left Distribution�

• distribution tapers more to the left than to the right
• has longer tail to the left compared to a much
• shorter right tail
• values are more concentrated above than below the

mean

• small values in the left tail will make the mean less

than the median

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Test of Skewness

• If mean, median and mode are not equal
• Sum of Positive Deviation from median are not equal to sum of negative deviation from median

Degree of Skewness

• If skewness is less than -1 or greater than 1, the distribution is highly skewed.
• If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed.
• If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.

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Difference between Variance and Skewness

• 1. Variance tells us about the amount of variability while skewness gives the direction of variability.
• 2. In business and economic series, measures of variation have greater practical application than measures of skewness. However, in medical and life science field measures of skewness have greater practical applications than the variance.

VARIOUS MEASURES OF SKEWNESS

Measures of skewness can be

• Absolute
• Relative.

Thank You

Absolute Measures of Skewness �

• 1. Skewness (Sk) = Mean – Median
• 2. Skewness (Sk) = Mean – Mode
• 3. Skewness (Sk) = (Q3 - Q2) - (Q2 - Q1)

Relative Measures of Skewness

• β and γ Coefficient of Skewness .

β ₁ = μ₃ ²

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μ₂³

Relative Measures of Skewness

• Karl Pearson’s Coefficient of Skewness

S_k = Mean – Mode

____________

σ

S_k = 3(Mean – Median)

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σ

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Relative Measures of Skewness

• Bowleys’s Coefficient of Skewness

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S_k =Q₃-2Q₂+Q₁

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(Q₃-Q₁)

Relative Measures of Skewness

Kelly’s Coefficient of Skewness

S_k = P₉₀ -2P₅₀+P₁₀

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(P₉₀-P₁₀)